Pub Date : 2023-10-13DOI: 10.1007/s00033-023-02110-w
Abhishek Chaudhary, Guy Vallet
Abstract In this article, we study the inviscid limit of the stochastic incompressible Navier–Stokes equations in three-dimensional space. We prove that a subsequence of weak martingale solutions of the stochastic incompressible Navier–Stokes equations converges strongly to a weak martingale solution of the stochastic incompressible Euler equations in the periodic domain under the well-accepted hypothesis, namely Kolmogorov hypothesis ( K41 ).
{"title":"A short remark on inviscid limit of the stochastic Navier–Stokes equations","authors":"Abhishek Chaudhary, Guy Vallet","doi":"10.1007/s00033-023-02110-w","DOIUrl":"https://doi.org/10.1007/s00033-023-02110-w","url":null,"abstract":"Abstract In this article, we study the inviscid limit of the stochastic incompressible Navier–Stokes equations in three-dimensional space. We prove that a subsequence of weak martingale solutions of the stochastic incompressible Navier–Stokes equations converges strongly to a weak martingale solution of the stochastic incompressible Euler equations in the periodic domain under the well-accepted hypothesis, namely Kolmogorov hypothesis ( K41 ).","PeriodicalId":54401,"journal":{"name":"Zeitschrift fur Angewandte Mathematik und Physik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135854826","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-13DOI: 10.1007/s00033-023-02108-4
Jaime E. Muñoz Rivera, Maria Grazia Naso
Abstract Bresse system over the interval (0, L ) with pointwise dissipation at $$xi in (0,{L})$$ ξ∈(0,L) is analyzed. The exponential stability of the related semigroup is shown provided the dissipative points are of the form $$xi in mathbb {Q}{L}$$ ξ∈QL and $$xi ne frac{n}{2m+1}L$$ ξ≠n2m+1L , where $$n,min mathbb {N}$$ n,m∈N and n , and $$2m+1$$ 2m+1 are co-prime.
摘要分析了区间(0,L)上具有点向耗散($$xi in (0,{L})$$ ξ∈(0,L)的Bresse系统。给出了相关半群的指数稳定性，其耗散点为$$xi in mathbb {Q}{L}$$ ξ∈Q L和$$xi ne frac{n}{2m+1}L$$ ξ≠n 2 m + 1 L，其中$$n,min mathbb {N}$$ n, m∈n和n, $$2m+1$$ 2 m + 1为共素数。
{"title":"Pointwise stabilization of Bresse systems","authors":"Jaime E. Muñoz Rivera, Maria Grazia Naso","doi":"10.1007/s00033-023-02108-4","DOIUrl":"https://doi.org/10.1007/s00033-023-02108-4","url":null,"abstract":"Abstract Bresse system over the interval (0, L ) with pointwise dissipation at $$xi in (0,{L})$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>ξ</mml:mi> <mml:mo>∈</mml:mo> <mml:mo>(</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mi>L</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> is analyzed. The exponential stability of the related semigroup is shown provided the dissipative points are of the form $$xi in mathbb {Q}{L}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>ξ</mml:mi> <mml:mo>∈</mml:mo> <mml:mi>Q</mml:mi> <mml:mi>L</mml:mi> </mml:mrow> </mml:math> and $$xi ne frac{n}{2m+1}L$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>ξ</mml:mi> <mml:mo>≠</mml:mo> <mml:mfrac> <mml:mi>n</mml:mi> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>m</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:mfrac> <mml:mi>L</mml:mi> </mml:mrow> </mml:math> , where $$n,min mathbb {N}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>,</mml:mo> <mml:mi>m</mml:mi> <mml:mo>∈</mml:mo> <mml:mi>N</mml:mi> </mml:mrow> </mml:math> and n , and $$2m+1$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>m</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> are co-prime.","PeriodicalId":54401,"journal":{"name":"Zeitschrift fur Angewandte Mathematik und Physik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135854842","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-06DOI: 10.1007/s00033-023-02097-4
Jinliang Wang, Meiyu Cao, Toshikazu Kuniya
Abstract In this paper, we will revisit the model studied in Lou and Zhao (J Math Biol 62:543–568, 2011), where the model takes the form of a nonlocal and time-delayed reaction–diffusion model arising from the fixed incubation period. We consider the infection age to be a continuous variable but without the limitation of the fixed incubation period, leading to an age-space structured malaria model in a bounded domain. By performing the elementary analysis, we investigate the well-posedness of the model by proving the global existence of the solution, define the explicit formula of basic reproduction number when all parameters remain constant. By analyzing the characteristic equations and designing suitable Lyapunov functions, we also establish the threshold dynamics of the constant disease-free and positive equilibria. Our theoretical results are also validated by numerical simulations for 1-dimensional and 2-dimensional domains.
在本文中，我们将重新审视Lou和Zhao (J Math Biol 62:543-568, 2011)所研究的模型，该模型采用由固定潜伏期引起的非局部延时反应扩散模型的形式。我们认为感染年龄是一个连续变量，但不受固定潜伏期的限制，从而在有界域中得到年龄空间结构的疟疾模型。通过初步分析，通过证明解的整体存在性，研究了模型的适定性，定义了所有参数保持不变时基本再现数的显式公式。通过分析特征方程和设计合适的Lyapunov函数，建立了常无病平衡点和正平衡点的阈值动力学。我们的理论结果也通过一维和二维的数值模拟得到了验证。
{"title":"Dynamical analysis of an age-space structured malaria epidemic model","authors":"Jinliang Wang, Meiyu Cao, Toshikazu Kuniya","doi":"10.1007/s00033-023-02097-4","DOIUrl":"https://doi.org/10.1007/s00033-023-02097-4","url":null,"abstract":"Abstract In this paper, we will revisit the model studied in Lou and Zhao (J Math Biol 62:543–568, 2011), where the model takes the form of a nonlocal and time-delayed reaction–diffusion model arising from the fixed incubation period. We consider the infection age to be a continuous variable but without the limitation of the fixed incubation period, leading to an age-space structured malaria model in a bounded domain. By performing the elementary analysis, we investigate the well-posedness of the model by proving the global existence of the solution, define the explicit formula of basic reproduction number when all parameters remain constant. By analyzing the characteristic equations and designing suitable Lyapunov functions, we also establish the threshold dynamics of the constant disease-free and positive equilibria. Our theoretical results are also validated by numerical simulations for 1-dimensional and 2-dimensional domains.","PeriodicalId":54401,"journal":{"name":"Zeitschrift fur Angewandte Mathematik und Physik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134944299","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-06DOI: 10.1007/s00033-023-02105-7
Jean Carlos Nakasato, Igor Pažanin
{"title":"Homogenization of the non-isothermal, non-Newtonian fluid flow in a thin domain with oscillating boundary","authors":"Jean Carlos Nakasato, Igor Pažanin","doi":"10.1007/s00033-023-02105-7","DOIUrl":"https://doi.org/10.1007/s00033-023-02105-7","url":null,"abstract":"","PeriodicalId":54401,"journal":{"name":"Zeitschrift fur Angewandte Mathematik und Physik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135351667","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-06DOI: 10.1007/s00033-023-02112-8
Rong Zhou, Shi-Liang Wu
{"title":"A two-strain malaria transmission model with seasonality and incubation period","authors":"Rong Zhou, Shi-Liang Wu","doi":"10.1007/s00033-023-02112-8","DOIUrl":"https://doi.org/10.1007/s00033-023-02112-8","url":null,"abstract":"","PeriodicalId":54401,"journal":{"name":"Zeitschrift fur Angewandte Mathematik und Physik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135352053","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-06DOI: 10.1007/s00033-023-02114-6
Changfeng Liu, Shangjiang Guo
{"title":"Global bounded solution of a forager–exploiter model with logistic sources and different taxis mechanisms","authors":"Changfeng Liu, Shangjiang Guo","doi":"10.1007/s00033-023-02114-6","DOIUrl":"https://doi.org/10.1007/s00033-023-02114-6","url":null,"abstract":"","PeriodicalId":54401,"journal":{"name":"Zeitschrift fur Angewandte Mathematik und Physik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135345422","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-06DOI: 10.1007/s00033-023-02103-9
Jie Zhang, Shu Wang, Fan Wu
{"title":"On Liouville-type theorems for the stationary nematic liquid crystal equations","authors":"Jie Zhang, Shu Wang, Fan Wu","doi":"10.1007/s00033-023-02103-9","DOIUrl":"https://doi.org/10.1007/s00033-023-02103-9","url":null,"abstract":"","PeriodicalId":54401,"journal":{"name":"Zeitschrift fur Angewandte Mathematik und Physik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135345428","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-06DOI: 10.1007/s00033-023-02109-3
Wen-Shuo Yuan, Bin Ge, Qing-Hai Cao, Yu Zhang
{"title":"The existence of solutions for parabolic problem with the limiting case of double phase flux","authors":"Wen-Shuo Yuan, Bin Ge, Qing-Hai Cao, Yu Zhang","doi":"10.1007/s00033-023-02109-3","DOIUrl":"https://doi.org/10.1007/s00033-023-02109-3","url":null,"abstract":"","PeriodicalId":54401,"journal":{"name":"Zeitschrift fur Angewandte Mathematik und Physik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135352267","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-06DOI: 10.1007/s00033-023-02101-x
Bogdan-Vasile Matioc, Georg Prokert
Abstract We consider the quasistationary Stokes flow that describes the motion of a two-dimensional fluid body under the influence of surface tension effects in an unbounded, infinite-bottom geometry. We reformulate the problem as a fully nonlinear parabolic evolution problem for the function that parameterizes the boundary of the fluid with the nonlinearities expressed in terms of singular integrals. We prove well-posedness of the problem in the subcritical Sobolev spaces $$H^s(mathbb {R})$$ Hs(R) up to critical regularity, and establish parabolic smoothing properties for the solutions. Moreover, we identify the problem as the singular limit of the two-phase quasistationary Stokes flow when the viscosity of one of the fluids vanishes.
我们考虑准静止斯托克斯流，它描述了在无界、无限底几何中受表面张力效应影响的二维流体的运动。我们将该问题重新表述为一个完全非线性抛物演化问题，该函数参数化流体边界，非线性以奇异积分形式表示。我们证明了问题在次临界Sobolev空间$$H^s(mathbb {R})$$ H s (R)上达到临界正则性的适定性，并建立了解的抛物平滑性质。此外，我们将问题确定为当其中一种流体的粘度消失时两相准静止斯托克斯流的奇异极限。
{"title":"Capillarity-driven Stokes flow: the one-phase problem as small viscosity limit","authors":"Bogdan-Vasile Matioc, Georg Prokert","doi":"10.1007/s00033-023-02101-x","DOIUrl":"https://doi.org/10.1007/s00033-023-02101-x","url":null,"abstract":"Abstract We consider the quasistationary Stokes flow that describes the motion of a two-dimensional fluid body under the influence of surface tension effects in an unbounded, infinite-bottom geometry. We reformulate the problem as a fully nonlinear parabolic evolution problem for the function that parameterizes the boundary of the fluid with the nonlinearities expressed in terms of singular integrals. We prove well-posedness of the problem in the subcritical Sobolev spaces $$H^s(mathbb {R})$$ <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:mi>R</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> up to critical regularity, and establish parabolic smoothing properties for the solutions. Moreover, we identify the problem as the singular limit of the two-phase quasistationary Stokes flow when the viscosity of one of the fluids vanishes.","PeriodicalId":54401,"journal":{"name":"Zeitschrift fur Angewandte Mathematik und Physik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135351838","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-03DOI: 10.1007/s00033-023-02072-z
Huashui Zhan
{"title":"Study of the stability to an anisotropic reaction–diffusion equation","authors":"Huashui Zhan","doi":"10.1007/s00033-023-02072-z","DOIUrl":"https://doi.org/10.1007/s00033-023-02072-z","url":null,"abstract":"","PeriodicalId":54401,"journal":{"name":"Zeitschrift fur Angewandte Mathematik und Physik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135690012","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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