Pub Date : 2023-11-13DOI: 10.1007/s44198-023-00152-2
Lifang Cheng, Ming Liu, Dongpo Hu, Litao Zhang
Abstract Bifurcations of equilibria of a wing model have been investigated in this paper. It is shown that the quintic nonlinear terms in the pitch and the plunge coordinate have affected the bifurcation structure of nontrivial equilibria in different degree. In contrast with the quintic stiffening parameter in plunge, the quintic parameter in pitch has a relatively significant effect, which will affect the number, position and stability of nontrivial equilibria. Therein two pairs of nontrivial equilibria with opposite stability coexist or disappear by two fold bifurcations. If the freestream velocity has been taken as a continuation parameter, it will affect the bifurcation structure of all the equilibria, including the trivial and the nontrivial. Wherein the equilibria vary from a trivial to two nontrivial ones by a pitchfork bifurcation. Then one of nontrivial equilibria experiences a supercritical Hopf bifurcation and the bifurcated limit cycles form an ellipsoidal structure with the limit cycles bifurcated from the trivial equilibrium.
{"title":"An Investigation of Dynamical Behavior of a Wing Model","authors":"Lifang Cheng, Ming Liu, Dongpo Hu, Litao Zhang","doi":"10.1007/s44198-023-00152-2","DOIUrl":"https://doi.org/10.1007/s44198-023-00152-2","url":null,"abstract":"Abstract Bifurcations of equilibria of a wing model have been investigated in this paper. It is shown that the quintic nonlinear terms in the pitch and the plunge coordinate have affected the bifurcation structure of nontrivial equilibria in different degree. In contrast with the quintic stiffening parameter in plunge, the quintic parameter in pitch has a relatively significant effect, which will affect the number, position and stability of nontrivial equilibria. Therein two pairs of nontrivial equilibria with opposite stability coexist or disappear by two fold bifurcations. If the freestream velocity has been taken as a continuation parameter, it will affect the bifurcation structure of all the equilibria, including the trivial and the nontrivial. Wherein the equilibria vary from a trivial to two nontrivial ones by a pitchfork bifurcation. Then one of nontrivial equilibria experiences a supercritical Hopf bifurcation and the bifurcated limit cycles form an ellipsoidal structure with the limit cycles bifurcated from the trivial equilibrium.","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":"52 16","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136348575","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-13DOI: 10.1007/s44198-023-00150-4
Donghao Li, Ling Liu, Hongwei Zhang
Abstract It is shown that solutions of the (relativistic) Vlasov–Maxwell system converge pointwise to solutions of the Vlasov–Poisson system globally in time at the asymptotic rate of $$c^{-1},$$ c-1, as the light speed c tends to infinity, which extends the results of Asano and Ukai (Stud Math Appl 18:369–383, 1986), Degond (Math Methods Appl Sci 8:533–558, 1986) and Schaeffer (Commun Math Phys 104:403–421, 1986). The analysis relies on the method of Glassey and Strauss (Commun Math Phys 113:191–208, 1987) and Schaeffer (Commun Math Phys 104:403–421, 1986).
摘要证明了(相对论性)Vlasov-Maxwell系统的解在时间上以$$c^{-1},$$ c - 1的渐近速率全局收敛于Vlasov-Poisson系统的解，当光速c趋于无穷大时，推广了Asano和Ukai (Stud数学应用，18:369-383,1986)，Degond(数学方法应用，8:533-558,1986)和Schaeffer(公共数学物理，104:404 - 421,1986)的结果。分析依据Glassey和Strauss (common Math Phys 113:191-208, 1987)和Schaeffer (common Math Phys 104:403-421, 1986)的方法。
{"title":"On Global Classical Limit of the (Relativistic) Vlasov–Maxwell System","authors":"Donghao Li, Ling Liu, Hongwei Zhang","doi":"10.1007/s44198-023-00150-4","DOIUrl":"https://doi.org/10.1007/s44198-023-00150-4","url":null,"abstract":"Abstract It is shown that solutions of the (relativistic) Vlasov–Maxwell system converge pointwise to solutions of the Vlasov–Poisson system globally in time at the asymptotic rate of $$c^{-1},$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msup> <mml:mi>c</mml:mi> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:mo>,</mml:mo> </mml:mrow> </mml:math> as the light speed c tends to infinity, which extends the results of Asano and Ukai (Stud Math Appl 18:369–383, 1986), Degond (Math Methods Appl Sci 8:533–558, 1986) and Schaeffer (Commun Math Phys 104:403–421, 1986). The analysis relies on the method of Glassey and Strauss (Commun Math Phys 113:191–208, 1987) and Schaeffer (Commun Math Phys 104:403–421, 1986).","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":"64 12","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136347305","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-31DOI: 10.1007/s44198-023-00148-y
Yuli Guo, Weiguo Zhang, Siyu Hong
Abstract In this paper, the orbital stability of solitary wave for Eckhaus–Kundu equation is studied. Since the equation we studied is difficult to be expressed as a standard Hamiltonian system, the Grillakis–Shatah–Strauss theory about the orbital stability of soliton solutions for nonlinear Hamiltonian systems cannot be directly applied. By constructing three new conserved quantities and using special techniques and detailed spectral analysis, the above difficulty is overcome, then we obtain the conclusion that the solitary wave of Eckhaus–Kundu equation is orbitally stable.
{"title":"Orbital Stability of Solitary Wave for Eckhaus–Kundu Equation","authors":"Yuli Guo, Weiguo Zhang, Siyu Hong","doi":"10.1007/s44198-023-00148-y","DOIUrl":"https://doi.org/10.1007/s44198-023-00148-y","url":null,"abstract":"Abstract In this paper, the orbital stability of solitary wave for Eckhaus–Kundu equation is studied. Since the equation we studied is difficult to be expressed as a standard Hamiltonian system, the Grillakis–Shatah–Strauss theory about the orbital stability of soliton solutions for nonlinear Hamiltonian systems cannot be directly applied. By constructing three new conserved quantities and using special techniques and detailed spectral analysis, the above difficulty is overcome, then we obtain the conclusion that the solitary wave of Eckhaus–Kundu equation is orbitally stable.","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":"71 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135814151","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-30DOI: 10.1007/s44198-023-00149-x
Ling Lei, Shou-Fu Tian, Yan-Qiang Wu
Abstract We investigate the multi-soliton solutions for the Cauchy problem of the nonlocal Kundu-nonlinear Schrödinger (NK-NLS) equation with step-like initial data. We first perform the spectral analysis on the Lax pair of the NK-NLS equation, and then establish the Riemann-Hilbert (RH) problem of the equation based on the analytic, symmetric and asymptotic properties of Jost solutions and spectral functions. Because of the influence of step-like initial value, we need to consider the singularity condition of the RH problem at the origin, and this singularity condition can be converted to a residue condition. Further, the multi-soliton solutions of the NK-NLS equation are obtained in terms of the corresponding RH problem.
{"title":"Multi-Soliton Solutions for the Nonlocal Kundu-Nonlinear Schrödinger Equation with Step-Like Initial Data","authors":"Ling Lei, Shou-Fu Tian, Yan-Qiang Wu","doi":"10.1007/s44198-023-00149-x","DOIUrl":"https://doi.org/10.1007/s44198-023-00149-x","url":null,"abstract":"Abstract We investigate the multi-soliton solutions for the Cauchy problem of the nonlocal Kundu-nonlinear Schrödinger (NK-NLS) equation with step-like initial data. We first perform the spectral analysis on the Lax pair of the NK-NLS equation, and then establish the Riemann-Hilbert (RH) problem of the equation based on the analytic, symmetric and asymptotic properties of Jost solutions and spectral functions. Because of the influence of step-like initial value, we need to consider the singularity condition of the RH problem at the origin, and this singularity condition can be converted to a residue condition. Further, the multi-soliton solutions of the NK-NLS equation are obtained in terms of the corresponding RH problem.","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":"37 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136022603","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-19DOI: 10.1007/s44198-023-00138-0
H. Amirzadeh-Fard, Gh. Haghighatdoost, A. Rezaei-Aghdam
Abstract By Poissonization of Jacobi structures on real three-dimensional Lie groups $${textbf{G}}$$ G and using the realizations of their Lie algebras, we obtain integrable bi-Hamiltonian systems on $${textbf{G}} otimes {mathbb {R}}$$ G⊗R .
{"title":"Integrable Bi-Hamiltonian Systems by Jacobi Structure on Real Three-Dimensional Lie Groups","authors":"H. Amirzadeh-Fard, Gh. Haghighatdoost, A. Rezaei-Aghdam","doi":"10.1007/s44198-023-00138-0","DOIUrl":"https://doi.org/10.1007/s44198-023-00138-0","url":null,"abstract":"Abstract By Poissonization of Jacobi structures on real three-dimensional Lie groups $${textbf{G}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>G</mml:mi> </mml:math> and using the realizations of their Lie algebras, we obtain integrable bi-Hamiltonian systems on $${textbf{G}} otimes {mathbb {R}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>G</mml:mi> <mml:mo>⊗</mml:mo> <mml:mi>R</mml:mi> </mml:mrow> </mml:math> .","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135730560","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-19DOI: 10.1007/s44198-023-00146-0
M. M. Khader, M. M. Babatin
Abstract This study aims to elucidates the effects of Ohmic dissipation and the magnetic field on the behavior of a Casson fluid flowing across a vertically stretched surface. The goal is to solve the problem by using numerical approaches. Furthermore, the fluid’s thermal conductivity is intended to vary proportionately with temperature. The effects of thermal radiation, electric fields, and viscous dissipation are taken into account in this study. A set of partial differential equations (PDEs) is used to quantitatively reflect the numerous physical conditions that are placed on the sheet’s surrounding wall as well as the processes of momentum and heat transport. A system of ordinary differential equations (ODEs) is created from the set of PDEs by using similarity transformations. The mathematical model of the problem is made easier by this conversion. Furthermore, this study’s main goal is to investigate the numerical treatment of the proposed model that takes Caputo fractional-order derivatives into account. The spectral collocation method is used to solve the system of ODEs that follow from the transformation. This approach efficiently solves the problem by approximating the solution of the ODEs using Chebyshev polynomials of the sixth kind. Several observations are made to evaluate the approach’s effectiveness, and the convergence of the method is studied. Visual representations of the effects of different parameters on the velocity and temperature profiles provide a thorough understanding of their effects. These graphical representations offer insightful views into how the system behaves in various scenarios. The results of this investigation suggest that the mixed convection parameter and the local electric parameter both boost the velocity field. Further, the temperature field is positively impacted by the slip velocity, thermal conductivity, and Eckert numbers. These findings imply that altering these variables will have an impact on the system’s fluid flow and heat transfer properties.
{"title":"Evaluating the Impacts of Thermal Conductivity on Casson Fluid Flow Near a Slippery Sheet: Numerical Simulation Using Sixth-Kind Chebyshev Polynomials","authors":"M. M. Khader, M. M. Babatin","doi":"10.1007/s44198-023-00146-0","DOIUrl":"https://doi.org/10.1007/s44198-023-00146-0","url":null,"abstract":"Abstract This study aims to elucidates the effects of Ohmic dissipation and the magnetic field on the behavior of a Casson fluid flowing across a vertically stretched surface. The goal is to solve the problem by using numerical approaches. Furthermore, the fluid’s thermal conductivity is intended to vary proportionately with temperature. The effects of thermal radiation, electric fields, and viscous dissipation are taken into account in this study. A set of partial differential equations (PDEs) is used to quantitatively reflect the numerous physical conditions that are placed on the sheet’s surrounding wall as well as the processes of momentum and heat transport. A system of ordinary differential equations (ODEs) is created from the set of PDEs by using similarity transformations. The mathematical model of the problem is made easier by this conversion. Furthermore, this study’s main goal is to investigate the numerical treatment of the proposed model that takes Caputo fractional-order derivatives into account. The spectral collocation method is used to solve the system of ODEs that follow from the transformation. This approach efficiently solves the problem by approximating the solution of the ODEs using Chebyshev polynomials of the sixth kind. Several observations are made to evaluate the approach’s effectiveness, and the convergence of the method is studied. Visual representations of the effects of different parameters on the velocity and temperature profiles provide a thorough understanding of their effects. These graphical representations offer insightful views into how the system behaves in various scenarios. The results of this investigation suggest that the mixed convection parameter and the local electric parameter both boost the velocity field. Further, the temperature field is positively impacted by the slip velocity, thermal conductivity, and Eckert numbers. These findings imply that altering these variables will have an impact on the system’s fluid flow and heat transfer properties.","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":"68 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135729670","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-18DOI: 10.1007/s44198-023-00144-2
Ming Li, Jianxia He
Abstract This paper is devoted to the stability and decay estimates of solutions to the two-dimensional magneto-micropolar fluid equations with partial dissipation. Firstly, focus on the 2D magneto-micropolar equation with only velocity dissipation and partial magnetic diffusion, we obtain the global existence of solutions with small initial in $$H^s({mathbb {R}}^2)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>H</mml:mi> <mml:mi>s</mml:mi> </mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:msup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> $$(s>1)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>s</mml:mi> <mml:mo>></mml:mo> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> , and by fully exploiting the special structure of the system and using the Fourier splitting methods, we establish the large time decay rates of solutions. Secondly, when the magnetic field has partial dissipation, we show the global existence of solutions with small initial data in $$dot{B}^0_{2,1}({mathbb {R}}^2)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup> <mml:mover> <mml:mi>B</mml:mi> <mml:mo>˙</mml:mo> </mml:mover> <mml:mrow> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:mn>0</mml:mn> </mml:msubsup> <mml:mrow> <mml:mo>(</mml:mo> <mml:msup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> . In addition, we explore the decay rates of these global solutions are correspondingly established in $$dot{B}^m_{2,1}({mathbb {R}}^2)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup> <mml:mover> <mml:mi>B</mml:mi> <mml:mo>˙</mml:mo> </mml:mover> <mml:mrow> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:mi>m</mml:mi> </mml:msubsup> <mml:mrow> <mml:mo>(</mml:mo> <mml:msup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> with $$0 le m le s$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>0</mml:mn> <mml:mo>≤</mml:mo> <mml:mi>m</mml:mi> <mml:mo>≤</mml:mo> <mml:mi>s</mml:mi> </mml:mrow> </mml:math> , when the initial data belongs to the negative Sobolev space $$dot{H}^{-l}({mathbb {R}}^2)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mover> <mml:mi>H</mml:mi> <mml:mo>˙</mml:mo> </mml:mover> <mml:mrow> <mml:mo>-</mml:mo> <mml:mi>l</mml:mi> </mml:mrow> </mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:msup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> (for each $$0 le l <1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>0</mml:mn> <mml:mo>≤</mml:m
摘要本文研究具有部分耗散的二维磁微极流体方程解的稳定性和衰减估计。首先，对只考虑速度耗散和部分磁扩散的二维磁微极方程，得到了在$$H^s({mathbb {R}}^2)$$ H s (R 2) $$(s>1)$$ (s ＆gt;1)，充分利用系统的特殊结构，利用傅里叶分裂方法，建立了解的大时间衰减率。其次，当磁场存在部分耗散时，我们在$$dot{B}^0_{2,1}({mathbb {R}}^2)$$ B˙2,10 (r2)中证明了具有小初始数据的解的整体存在性。此外，我们还探讨了当初始数据属于负Sobolev空间$$dot{H}^{-l}({mathbb {R}}^2)$$ H˙l (r2)时，这些全局解的衰减率对应地建立在$$dot{B}^m_{2,1}({mathbb {R}}^2)$$ B˙2,1 m (r2)中，$$0 le m le s$$ 0≤m≤s(对于每个$$0 le l <1$$ 0≤l ＆lt;1)。
{"title":"Large Time Behavior and Stability for Two-Dimensional Magneto-Micropolar Equations with Partial Dissipation","authors":"Ming Li, Jianxia He","doi":"10.1007/s44198-023-00144-2","DOIUrl":"https://doi.org/10.1007/s44198-023-00144-2","url":null,"abstract":"Abstract This paper is devoted to the stability and decay estimates of solutions to the two-dimensional magneto-micropolar fluid equations with partial dissipation. Firstly, focus on the 2D magneto-micropolar equation with only velocity dissipation and partial magnetic diffusion, we obtain the global existence of solutions with small initial in $$H^s({mathbb {R}}^2)$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msup> <mml:mi>H</mml:mi> <mml:mi>s</mml:mi> </mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:msup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> $$(s>1)$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>s</mml:mi> <mml:mo>></mml:mo> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> , and by fully exploiting the special structure of the system and using the Fourier splitting methods, we establish the large time decay rates of solutions. Secondly, when the magnetic field has partial dissipation, we show the global existence of solutions with small initial data in $$dot{B}^0_{2,1}({mathbb {R}}^2)$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msubsup> <mml:mover> <mml:mi>B</mml:mi> <mml:mo>˙</mml:mo> </mml:mover> <mml:mrow> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:mn>0</mml:mn> </mml:msubsup> <mml:mrow> <mml:mo>(</mml:mo> <mml:msup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> . In addition, we explore the decay rates of these global solutions are correspondingly established in $$dot{B}^m_{2,1}({mathbb {R}}^2)$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msubsup> <mml:mover> <mml:mi>B</mml:mi> <mml:mo>˙</mml:mo> </mml:mover> <mml:mrow> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:mi>m</mml:mi> </mml:msubsup> <mml:mrow> <mml:mo>(</mml:mo> <mml:msup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> with $$0 le m le s$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mn>0</mml:mn> <mml:mo>≤</mml:mo> <mml:mi>m</mml:mi> <mml:mo>≤</mml:mo> <mml:mi>s</mml:mi> </mml:mrow> </mml:math> , when the initial data belongs to the negative Sobolev space $$dot{H}^{-l}({mathbb {R}}^2)$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msup> <mml:mover> <mml:mi>H</mml:mi> <mml:mo>˙</mml:mo> </mml:mover> <mml:mrow> <mml:mo>-</mml:mo> <mml:mi>l</mml:mi> </mml:mrow> </mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:msup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> (for each $$0 le l <1$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mn>0</mml:mn> <mml:mo>≤</mml:m","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135884418","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-16DOI: 10.1007/s44198-023-00145-1
M. Ferdows, Abid Hossain, M. J. Uddin, Fahiza Tabassum Mim, Shuyu Sun
Abstract The viscous laminar magnetohydrodynamic convective boundary layer flow with the combined effects of chemical reaction and nonlinear velocity slip and linear thermal and concentration slips have been considered across a flat plate in motion. Using a non-dimensional transformation attained by the single parameter continuous group method, the governing equations are transformed into a system of nonlinear ordinary similarity equations, then, the solutions of the coupled system of equations are constructed for velocity, temperature, and concentration functions by using the numerical methods. Among the parameters that have been looked at are the buoyancy parameter N, the nonlinear slip parameter $${mathrm{n}}_{1}$$ n1 , the order of chemical reaction n, the Prandtl number Pr, and the Schmidt number Sc. An investigation was made on the profiles with respect to mixed convection parameter $$uplambda $$ λ , order of chemical reaction n, arbitrary index parameter $${mathrm{n}}_{1}$$ n1 , velocity slip parameter a, thermal slip parameter b, mass slip parameter c, suction parameter fw, magnetic parameter M. Verification of the results were possible due to comparison of two numerical methods to obtain the solution to the differential equations. The present study indicates that, for a range of values of the magnetic parameter, the wall shear stress decreases with increasing mixed convection. Moreover, for a variety of mixed convection parameter instances, the wall heat transfer decreases with increasing perpendicular magnetic effect.
摘要研究了在运动平板上具有化学反应、非线性速度滑移和线性热、浓度滑移共同作用的粘性层流磁流体动力对流边界层流动。利用单参数连续群法得到的无量纲变换，将控制方程转化为非线性普通相似方程组，然后用数值方法构造速度、温度和浓度函数耦合方程组的解。研究的参数包括浮力参数N、非线性滑移参数$${mathrm{n}}_{1}$$ N 1、化学反应阶数N、普朗特数Pr和施密特数Sc。研究了混合对流参数$$uplambda $$ λ、化学反应阶数N、任意指标参数$${mathrm{n}}_{1}$$ N 1、速度滑移参数a、热滑移参数b、质量滑移参数c、通过比较两种数值方法求得的微分方程的解，可以对结果进行验证。研究表明，在一定的磁参量范围内，壁面剪切应力随混合对流的增大而减小。在多种混合对流参数情况下，壁面换热随垂直磁效应的增大而减小。
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Pub Date : 2023-10-10DOI: 10.1007/s44198-023-00147-z
Sheng-Nan Wang, Guo-Fu Yu, Zuo-Nong Zhu
Abstract In this paper, we investigate solutions of a (2+1)-dimensional sinh-Gordon equation. General solitons and (semi-)rational solutions are derived by the combination of Hirota’s bilinear method and Kadomtsev-Petviashvili hierarchy reduction approach. General solutions are expressed as $$Ntimes N$$ N×N Gram-type determinants. When the determinant size N is even, we generate solitons, line breathers, and (semi-)rational solutions located on constant backgrounds. In particular, through the asymptotic analysis we prove that the collision of solitons are completely elastic. When N is odd, we derive exact solutions on periodic backgrounds. The dynamical behaviors of those derived solutions are analyzed with plots. For rational solutions, we display the interaction of lumps. For semi-rational solutions, we find the interaction solutions between lumps and solitons.
摘要本文研究了一类(2+1)维sinh-Gordon方程的解。结合Hirota的双线性方法和Kadomtsev-Petviashvili层次约简方法，导出了一般孤子和(半)有理解。通解表示为$$Ntimes N$$ N × N gram型行列式。当行列式大小N为偶数时，我们生成位于恒定背景上的孤子、线呼吸子和(半)有理解。特别地，我们通过渐近分析证明了孤子的碰撞是完全弹性的。当N为奇数时，我们得到周期背景下的精确解。用图表分析了这些解的动力学行为。对于有理解，我们展示了块的相互作用。对于半有理解，我们找到了块与孤子之间的相互作用解。
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Pub Date : 2023-10-05DOI: 10.1007/s44198-023-00142-4
W. Abbas, M. A. Ibrahim, O. Mokhtar, Ahmed M. Megahed, Ahmed A. M. Said
Abstract Nanoparticles have the ability to increase the impact of convective heat transfer in the boundary layer region. An investigation is made to analysis of magnetohdrodynamic nanofluid flow with heat and mass transfer over a vertical cone in porous media under the impact of thermal radiations and chemical reaction. In addition, thermal radiations, Hall current, and viscous and Joule dissipations and chemical reaction effects are considered. Considered three different nanoparticles types namely copper, silver, and titanium dioxide with water as base fluid. The governing equations are transformed by similarity transformations into a set of non-linear ordinary differential equations involving variable coefficients. Two numerically approaches are used to solve the transformed boundary layer system Finite Difference Method (FDM) and Chebyshev-Galerkin Method (CGM). As stated in the present analysis, it is appropriate to address a number of physical mechanisms, including velocity, temperature and concentration, as well as closed-form skin friction/mass transfer/heat transfer coefficients. Different comparisons are done with previously published data in order to validate the current study under specific special circumstances, and it is determined that there is a very high degree of agreement. The main results indicated that as the Prandtl number increases, the temperature profile decreases, but it grows for higher values of the thermophoresis parameter, Brownian motion, and Eckert number. Moreover, higher Brownian motion values lead to a less prominent concentration profile. Consequently, this speeds up the cooling process and enhances the surface’s durability and strength.
{"title":"Numerical Analysis of MHD Nanofluid Flow Characteristics with Heat and Mass Transfer over a Vertical Cone Subjected to Thermal Radiations and Chemical Reaction","authors":"W. Abbas, M. A. Ibrahim, O. Mokhtar, Ahmed M. Megahed, Ahmed A. M. Said","doi":"10.1007/s44198-023-00142-4","DOIUrl":"https://doi.org/10.1007/s44198-023-00142-4","url":null,"abstract":"Abstract Nanoparticles have the ability to increase the impact of convective heat transfer in the boundary layer region. An investigation is made to analysis of magnetohdrodynamic nanofluid flow with heat and mass transfer over a vertical cone in porous media under the impact of thermal radiations and chemical reaction. In addition, thermal radiations, Hall current, and viscous and Joule dissipations and chemical reaction effects are considered. Considered three different nanoparticles types namely copper, silver, and titanium dioxide with water as base fluid. The governing equations are transformed by similarity transformations into a set of non-linear ordinary differential equations involving variable coefficients. Two numerically approaches are used to solve the transformed boundary layer system Finite Difference Method (FDM) and Chebyshev-Galerkin Method (CGM). As stated in the present analysis, it is appropriate to address a number of physical mechanisms, including velocity, temperature and concentration, as well as closed-form skin friction/mass transfer/heat transfer coefficients. Different comparisons are done with previously published data in order to validate the current study under specific special circumstances, and it is determined that there is a very high degree of agreement. The main results indicated that as the Prandtl number increases, the temperature profile decreases, but it grows for higher values of the thermophoresis parameter, Brownian motion, and Eckert number. Moreover, higher Brownian motion values lead to a less prominent concentration profile. Consequently, this speeds up the cooling process and enhances the surface’s durability and strength.","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135480700","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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