Pub Date : 2023-10-19DOI: 10.1080/00036811.2023.2271945
Xueliang Duan, Xiaofan Wu, Gongming Wei, Haitao Yang
AbstractThis paper deals with the following critical Choquard equation with a Kirchhoff type perturbation in bounded domains, {−(1+b‖u‖2)Δu=(∫Ωu2(y)|x−y|4dy)u+λuinΩ,u=0on∂Ω,where Ω⊂RN(N≥5) is a smooth bounded domain and ‖⋅‖ is the standard norm of H01(Ω). Under the suitable assumptions on the constant b≥0, we prove the existence of solutions for 0<λ≤λ1, where λ1>0 is the first eigenvalue of −Δ on Ω. Moreover, we prove the multiplicity of solutions for λ>λ1 and b>0 in suitable intervals.Keywords: Choquard equationKirchhoff problemcritical exponentNehari manifoldexistenceMathematic Subject classifications: 35A1535J60 Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis research is supported by Key Scientific Research Projects of Colleges and Universities in Henan Province [grant number 23A110018].
{"title":"The critical Choquard equations with a Kirchhoff type perturbation in bounded domains","authors":"Xueliang Duan, Xiaofan Wu, Gongming Wei, Haitao Yang","doi":"10.1080/00036811.2023.2271945","DOIUrl":"https://doi.org/10.1080/00036811.2023.2271945","url":null,"abstract":"AbstractThis paper deals with the following critical Choquard equation with a Kirchhoff type perturbation in bounded domains, {−(1+b‖u‖2)Δu=(∫Ωu2(y)|x−y|4dy)u+λuinΩ,u=0on∂Ω,where Ω⊂RN(N≥5) is a smooth bounded domain and ‖⋅‖ is the standard norm of H01(Ω). Under the suitable assumptions on the constant b≥0, we prove the existence of solutions for 0<λ≤λ1, where λ1>0 is the first eigenvalue of −Δ on Ω. Moreover, we prove the multiplicity of solutions for λ>λ1 and b>0 in suitable intervals.Keywords: Choquard equationKirchhoff problemcritical exponentNehari manifoldexistenceMathematic Subject classifications: 35A1535J60 Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis research is supported by Key Scientific Research Projects of Colleges and Universities in Henan Province [grant number 23A110018].","PeriodicalId":55507,"journal":{"name":"Applicable Analysis","volume":"69 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":"135778695","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-18DOI: 10.1080/00036811.2022.2036335
Munirah Alotaibi, Mohamed Jleli, Maria Alessandra Ragusa, Bessem Samet
AbstractIn this paper, an initial value problem for a nonlinear time-fractional Schrödinger equation with a singular logarithmic potential term is investigated. The considered problem involves the left/forward Hadamard-Caputo fractional derivative with respect to the time variable. Using the test function method with a judicious choice of the test function, we obtain sufficient criteria for the absence of global weak solutions.KEYWORDS: Nonlinear time-fractional Schrödinger equationsingular logarithmic potentialglobal weak solutionnonexistence2010 MATHEMATICS SUBJECT CLASSIFICATIONS: 35B4435B3326A33 Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThe third author wish to thank Faculty of Fundamental Science, Industrial University of Ho Chi Minh City, Vietnam, for the opportunity to work in it. The fourth author is supported by Researchers Supporting Project number (RSP-2021/4), King Saud University, Riyadh, Saudi Arabia.
{"title":"On the absence of global weak solutions for a nonlinear time-fractional Schrödinger equation","authors":"Munirah Alotaibi, Mohamed Jleli, Maria Alessandra Ragusa, Bessem Samet","doi":"10.1080/00036811.2022.2036335","DOIUrl":"https://doi.org/10.1080/00036811.2022.2036335","url":null,"abstract":"AbstractIn this paper, an initial value problem for a nonlinear time-fractional Schrödinger equation with a singular logarithmic potential term is investigated. The considered problem involves the left/forward Hadamard-Caputo fractional derivative with respect to the time variable. Using the test function method with a judicious choice of the test function, we obtain sufficient criteria for the absence of global weak solutions.KEYWORDS: Nonlinear time-fractional Schrödinger equationsingular logarithmic potentialglobal weak solutionnonexistence2010 MATHEMATICS SUBJECT CLASSIFICATIONS: 35B4435B3326A33 Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThe third author wish to thank Faculty of Fundamental Science, Industrial University of Ho Chi Minh City, Vietnam, for the opportunity to work in it. The fourth author is supported by Researchers Supporting Project number (RSP-2021/4), King Saud University, Riyadh, Saudi Arabia.","PeriodicalId":55507,"journal":{"name":"Applicable Analysis","volume":"19 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":"135888044","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-18DOI: 10.1080/00036811.2023.2271967
M. T. Jenaliyev, M. G. Yergaliyev
AbstractIn this paper, we study the solvability of one initial-boundary value problem for the Burgers equation with periodic boundary conditions in a nonlinearly degenerating domain. In this paper, we found an orthonormal basis for domains with time-varying boundaries. On this basis, we use the Faedo–Galerkin method to prove theorems about the unique solvability of the problem under consideration. We also present some numerical results in the form of graphs of solutions to the problem under study for various initial data.Keywords: Burgers equationperiodic boundary conditionsdegenerating domainGalerkin methodMathematics Subject Classifications: 35K5535K1035R37 Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThe research of the second author was supported by the grant of the Science Committee of the Ministry of Science and Higher Education of the Republic of Kazakhstan, Project AP13067805. The research of the first author was supported by the grant of the Science Committee of the Ministry of Science and Higher Education of the Republic of Kazakhstan, Project AP09258892.
{"title":"On initial-boundary value problem for the Burgers equation in nonlinearly degenerating domain","authors":"M. T. Jenaliyev, M. G. Yergaliyev","doi":"10.1080/00036811.2023.2271967","DOIUrl":"https://doi.org/10.1080/00036811.2023.2271967","url":null,"abstract":"AbstractIn this paper, we study the solvability of one initial-boundary value problem for the Burgers equation with periodic boundary conditions in a nonlinearly degenerating domain. In this paper, we found an orthonormal basis for domains with time-varying boundaries. On this basis, we use the Faedo–Galerkin method to prove theorems about the unique solvability of the problem under consideration. We also present some numerical results in the form of graphs of solutions to the problem under study for various initial data.Keywords: Burgers equationperiodic boundary conditionsdegenerating domainGalerkin methodMathematics Subject Classifications: 35K5535K1035R37 Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThe research of the second author was supported by the grant of the Science Committee of the Ministry of Science and Higher Education of the Republic of Kazakhstan, Project AP13067805. The research of the first author was supported by the grant of the Science Committee of the Ministry of Science and Higher Education of the Republic of Kazakhstan, Project AP09258892.","PeriodicalId":55507,"journal":{"name":"Applicable Analysis","volume":"5 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":"135888714","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-18DOI: 10.1080/00036811.2023.2269967
Jianjun Nie, Quanqing Li
AbstractIn this paper, we study the following critical nonlinear Schrödinger–Kirchhoff equation: ($P$) {−(a+b∫RN|∇u|2dx)Δu+V(x)u=P(x)|u|2∗−2u+μ|u|q−2u, in RN,u∈H1(RN)($P$) where a,b,μ>0, N≥3, max{2∗−1,2}0 and P(x)≥0 are two continuous functions. By using the variational method and truncation technique, we prove the multiplicity of solutions for Equation (P).Keywords: Schrödinger–Kirchhoff equationcritical exponentlocal Pohozaev identitiesmultiplicity of solutions2020 Mathematics Subject Classifications: 35J1047J30 Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis work is supported by the National Natural Science Foundation of China [grant numbers 12261031, 12261076, 11801545] and the Fundamental Research Funds for the Central Universities [grant number 2023MS078].
{"title":"Multiplicity of solutions for a critical nonlinear Schrödinger–Kirchhoff-type equation","authors":"Jianjun Nie, Quanqing Li","doi":"10.1080/00036811.2023.2269967","DOIUrl":"https://doi.org/10.1080/00036811.2023.2269967","url":null,"abstract":"AbstractIn this paper, we study the following critical nonlinear Schrödinger–Kirchhoff equation: ($P$) {−(a+b∫RN|∇u|2dx)Δu+V(x)u=P(x)|u|2∗−2u+μ|u|q−2u, in RN,u∈H1(RN)($P$) where a,b,μ>0, N≥3, max{2∗−1,2}<q<2∗=2NN−2, V(x)>0 and P(x)≥0 are two continuous functions. By using the variational method and truncation technique, we prove the multiplicity of solutions for Equation (P).Keywords: Schrödinger–Kirchhoff equationcritical exponentlocal Pohozaev identitiesmultiplicity of solutions2020 Mathematics Subject Classifications: 35J1047J30 Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis work is supported by the National Natural Science Foundation of China [grant numbers 12261031, 12261076, 11801545] and the Fundamental Research Funds for the Central Universities [grant number 2023MS078].","PeriodicalId":55507,"journal":{"name":"Applicable Analysis","volume":"1 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":"135883269","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-18DOI: 10.1080/00036811.2023.2271533
Xiuping Ye, Xueyun Lin
AbstractIn this paper, we investigate the well-posedness and large time behavior of solutions to the 3D incompressible magneto-micropolar equations. By virtue of the Lp−Lq estimate obtained through the spectral decomposition of the linearized magneto-micropolar equations, we show the existence and uniqueness of small L3-strong solutions of the equations with small initial data. Then basing on this result, we derive sharp time decay estimates of the L3-strong solutions.Keywords: 3D magneto-micropolar equationsspectral decompositionbanach contraction mapping principlelarge time decayMathematics Subject Classifications: 35B4035Q3535Q30 AcknowledgmentsThe authors are grateful to the anonymous referees for the kind suggestions that improved this paper.Disclosure statementThe authors do not have any relevant financial or non-financial competing interests. On behalf of all authors, the corresponding author states that there is no conflict of interest.Data availabilityData sharing is not applicable to this article as no datasets were generated or analyzed during the current study.
{"title":"Decay estimates of the 3D magneto-micropolar system with applications to L <sub>3</sub> -strong solutions","authors":"Xiuping Ye, Xueyun Lin","doi":"10.1080/00036811.2023.2271533","DOIUrl":"https://doi.org/10.1080/00036811.2023.2271533","url":null,"abstract":"AbstractIn this paper, we investigate the well-posedness and large time behavior of solutions to the 3D incompressible magneto-micropolar equations. By virtue of the Lp−Lq estimate obtained through the spectral decomposition of the linearized magneto-micropolar equations, we show the existence and uniqueness of small L3-strong solutions of the equations with small initial data. Then basing on this result, we derive sharp time decay estimates of the L3-strong solutions.Keywords: 3D magneto-micropolar equationsspectral decompositionbanach contraction mapping principlelarge time decayMathematics Subject Classifications: 35B4035Q3535Q30 AcknowledgmentsThe authors are grateful to the anonymous referees for the kind suggestions that improved this paper.Disclosure statementThe authors do not have any relevant financial or non-financial competing interests. On behalf of all authors, the corresponding author states that there is no conflict of interest.Data availabilityData sharing is not applicable to this article as no datasets were generated or analyzed during the current study.","PeriodicalId":55507,"journal":{"name":"Applicable Analysis","volume":"70 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":"135883831","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-16DOI: 10.1080/00036811.2023.2268636
Claudia Gariboldi, Anna Ochal, Mircea Sofonea, Domingo A. Tarzia
AbstractWe consider an elliptic variational inequality with unilateral constraints in a Hilbert space X which, under appropriate assumptions on the data, has a unique solution u. We formulate a convergence criterion to the solution u, i.e. we provide necessary and sufficient conditions on a sequence {un}⊂X which guarantee the convergence un→u in the space X. Then we illustrate the use of this criterion to recover well-known convergence results and well-posedness results in the sense of Tykhonov and Levitin–Polyak. We also provide two applications of our results, in the study of a heat transfer problem and an elastic frictionless contact problem, respectively.Keywords: Elliptic variational inequalityconvergence criterionconvergence resultswell-posednesscontactheat transferunilateral constraint2010 MSC: 47J2049J4040A0574M1574M1035J20 AcknowledgmentsThis project has received funding from the European Union's Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie Grant Agreement No. 823731 CONMECH. The second author was also supported by the Ministry of Science and Higher Education of Republic of Poland under Grant No. 440328/PnH2/2019, and in part from National Science Centre, Poland under project OPUS no. 2021/41/B/ST1/01636.Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis work was supported by European Commission[].
{"title":"A convergence criterion for elliptic variational inequalities","authors":"Claudia Gariboldi, Anna Ochal, Mircea Sofonea, Domingo A. Tarzia","doi":"10.1080/00036811.2023.2268636","DOIUrl":"https://doi.org/10.1080/00036811.2023.2268636","url":null,"abstract":"AbstractWe consider an elliptic variational inequality with unilateral constraints in a Hilbert space X which, under appropriate assumptions on the data, has a unique solution u. We formulate a convergence criterion to the solution u, i.e. we provide necessary and sufficient conditions on a sequence {un}⊂X which guarantee the convergence un→u in the space X. Then we illustrate the use of this criterion to recover well-known convergence results and well-posedness results in the sense of Tykhonov and Levitin–Polyak. We also provide two applications of our results, in the study of a heat transfer problem and an elastic frictionless contact problem, respectively.Keywords: Elliptic variational inequalityconvergence criterionconvergence resultswell-posednesscontactheat transferunilateral constraint2010 MSC: 47J2049J4040A0574M1574M1035J20 AcknowledgmentsThis project has received funding from the European Union's Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie Grant Agreement No. 823731 CONMECH. The second author was also supported by the Ministry of Science and Higher Education of Republic of Poland under Grant No. 440328/PnH2/2019, and in part from National Science Centre, Poland under project OPUS no. 2021/41/B/ST1/01636.Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis work was supported by European Commission[].","PeriodicalId":55507,"journal":{"name":"Applicable Analysis","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136114499","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-16DOI: 10.1080/00036811.2023.2270214
Guangbin Wang, Jingliang Lv, Xiaoling Zou
AbstractIn this paper, we study three stochastic two-species models. We construct the stochastic models corresponding to its deterministic model by introducing stochastic noise into the equations. For the first model, we show that the system has a unique global solution starting from the positive initial value. In addition, we discuss the extinction and the existence of stationary distribution under some conditions. For the second system, we explore the existence and uniqueness of the solution. Then we obtain sufficient conditions for global asymptotic stability of the equilibrium point and the positive recurrence of solution. For the last model, the existence and uniqueness of solution, the sufficient conditions for extinction and asymptotic stability and the positive recurrence of solution and weak persistence are derived. And numerical simulations are performed to support our results.Keywords: Stabilityextinctionstationary distributionpositive recurrenceweak persistenceMathematics Subject Classifications: 60G1560G4460G5260H10 Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis research was supported by Natural Science Foundation of Shandong Province, China [grant number ZR2020MA038] and [grant number ZR2020MA037].
{"title":"Dynamical analysis on stochastic two-species models","authors":"Guangbin Wang, Jingliang Lv, Xiaoling Zou","doi":"10.1080/00036811.2023.2270214","DOIUrl":"https://doi.org/10.1080/00036811.2023.2270214","url":null,"abstract":"AbstractIn this paper, we study three stochastic two-species models. We construct the stochastic models corresponding to its deterministic model by introducing stochastic noise into the equations. For the first model, we show that the system has a unique global solution starting from the positive initial value. In addition, we discuss the extinction and the existence of stationary distribution under some conditions. For the second system, we explore the existence and uniqueness of the solution. Then we obtain sufficient conditions for global asymptotic stability of the equilibrium point and the positive recurrence of solution. For the last model, the existence and uniqueness of solution, the sufficient conditions for extinction and asymptotic stability and the positive recurrence of solution and weak persistence are derived. And numerical simulations are performed to support our results.Keywords: Stabilityextinctionstationary distributionpositive recurrenceweak persistenceMathematics Subject Classifications: 60G1560G4460G5260H10 Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis research was supported by Natural Science Foundation of Shandong Province, China [grant number ZR2020MA038] and [grant number ZR2020MA037].","PeriodicalId":55507,"journal":{"name":"Applicable Analysis","volume":"218 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136113575","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 10.1080/00036811.2023.2268659
Jann-Long Chern, Masato Hashizume, Gyeongha Hwang
AbstractMotivated by the Hardy-Sobolev inequality with multiple Hardy potentials, we consider the following minimization problem : inf{|u|2s∗|x|s∫Ω|∇u|2dx−λ1∫Ωu2|x−P1|2dx−λ2∫Ωu2|x−P2|2dx|u∈H01(Ω),∫Ω|u|2s∗|x|sdx=1}where N≥3, Ω is a smooth domain, λ1,λ2∈R, 0,P1,P2∈Ω, s∈(0,2) and 2s∗=2(N−s)N−2. Concerning the coefficients of Hardy potentials, we derive a sharp threshold for the existence and non-existence of a minimizer. In addition, we study the existence and non-existence of a positive solution to the Euler-Lagrangian equations corresponding to the minimization problems.Keywords: Semilinear elliptic equationexistencenon-existenceminimizers of Hardy-Sobolev type inequalityHardy potentialMathematic Subject classifications: 35J2035J61 Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThe first author is supported by NSTC of Taiwan, Grant Number NSTC 110-2115-M-003-019-MY3 and NSTC 111-2218-E-008-004-MBK. The second author is supported by Grant-in-Aid for JSPS Research Fellow (JSPS KAKENHI Grant Number JP19K14571) and Osaka Central Advanced Mathematical Institute: MEXT Joint Usage/Research Center on Mathematics and Theoretical Physics JPMXP0619217849. The third author is supported by the 2020 Yeungnam University Research Grant. The authors thank Professors Futoshi Takahashi and Megumi Sano for their helpful comments on the results.
{"title":"Existence and non-existence of minimizers for Hardy-Sobolev type inequality with Hardy potentials","authors":"Jann-Long Chern, Masato Hashizume, Gyeongha Hwang","doi":"10.1080/00036811.2023.2268659","DOIUrl":"https://doi.org/10.1080/00036811.2023.2268659","url":null,"abstract":"AbstractMotivated by the Hardy-Sobolev inequality with multiple Hardy potentials, we consider the following minimization problem : inf{|u|2s∗|x|s∫Ω|∇u|2dx−λ1∫Ωu2|x−P1|2dx−λ2∫Ωu2|x−P2|2dx|u∈H01(Ω),∫Ω|u|2s∗|x|sdx=1}where N≥3, Ω is a smooth domain, λ1,λ2∈R, 0,P1,P2∈Ω, s∈(0,2) and 2s∗=2(N−s)N−2. Concerning the coefficients of Hardy potentials, we derive a sharp threshold for the existence and non-existence of a minimizer. In addition, we study the existence and non-existence of a positive solution to the Euler-Lagrangian equations corresponding to the minimization problems.Keywords: Semilinear elliptic equationexistencenon-existenceminimizers of Hardy-Sobolev type inequalityHardy potentialMathematic Subject classifications: 35J2035J61 Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThe first author is supported by NSTC of Taiwan, Grant Number NSTC 110-2115-M-003-019-MY3 and NSTC 111-2218-E-008-004-MBK. The second author is supported by Grant-in-Aid for JSPS Research Fellow (JSPS KAKENHI Grant Number JP19K14571) and Osaka Central Advanced Mathematical Institute: MEXT Joint Usage/Research Center on Mathematics and Theoretical Physics JPMXP0619217849. The third author is supported by the 2020 Yeungnam University Research Grant. The authors thank Professors Futoshi Takahashi and Megumi Sano for their helpful comments on the results.","PeriodicalId":55507,"journal":{"name":"Applicable Analysis","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135854223","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-12DOI: 10.1080/00036811.2023.2268634
Baoquan Yuan, Xueli Ke
ABSTRACTIn this paper, the local existence and uniqueness of weak solutions to a d-dimensional non-resistive MHD equations in homogeneous Besov spaces are studied. Specifically we obtain the local existence of a weak solution (u,b) of the non-resistive MHD equations for the initial data u0∈B˙p,1dp−1(Rd) and b0∈B˙p,1dp(Rd) with 1≤p≤∞, and the uniqueness of the weak solution when 1≤p≤2d. Compared with the previous results for the non-resistive MHD equations, in the local existence part, the range of p extends to 1≤p≤∞ from 1≤p≤2d, but the uniqueness of the solution requires 1≤p≤2d yet.KEYWORDS: Non-resistive MHD equationshomogeneous Besov spaceuniquenessweak solutionMATHEMATIC SUBJECT CLASSIFICATIONS (2000): 35Q3576D0376W05 Disclosure statementNo potential conflict of interest was reported by the author(s).Data availability statementData sharing not applicable to this article as no datasets were generated or analysed during the current study.Additional informationFundingThe work of B. Yuan was partially supported by the Innovative Research Team of Henan Polytechnic University [grant number T2022-7], and double first-class discipline project [grant number AQ20230775].
{"title":"Unique local weak solutions of the non-resistive MHD equations in homogeneous Besov space","authors":"Baoquan Yuan, Xueli Ke","doi":"10.1080/00036811.2023.2268634","DOIUrl":"https://doi.org/10.1080/00036811.2023.2268634","url":null,"abstract":"ABSTRACTIn this paper, the local existence and uniqueness of weak solutions to a d-dimensional non-resistive MHD equations in homogeneous Besov spaces are studied. Specifically we obtain the local existence of a weak solution (u,b) of the non-resistive MHD equations for the initial data u0∈B˙p,1dp−1(Rd) and b0∈B˙p,1dp(Rd) with 1≤p≤∞, and the uniqueness of the weak solution when 1≤p≤2d. Compared with the previous results for the non-resistive MHD equations, in the local existence part, the range of p extends to 1≤p≤∞ from 1≤p≤2d, but the uniqueness of the solution requires 1≤p≤2d yet.KEYWORDS: Non-resistive MHD equationshomogeneous Besov spaceuniquenessweak solutionMATHEMATIC SUBJECT CLASSIFICATIONS (2000): 35Q3576D0376W05 Disclosure statementNo potential conflict of interest was reported by the author(s).Data availability statementData sharing not applicable to this article as no datasets were generated or analysed during the current study.Additional informationFundingThe work of B. Yuan was partially supported by the Innovative Research Team of Henan Polytechnic University [grant number T2022-7], and double first-class discipline project [grant number AQ20230775].","PeriodicalId":55507,"journal":{"name":"Applicable Analysis","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136012904","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-11DOI: 10.1080/00036811.2023.2260406
Jianjun Huang, Zhenglu Jiang
AbstractWe study the spatially homogeneous solutions for the relativistic kinetic equations. It is shown that the Cauchy problem for the relativistic Boltzmann and Landau equation with soft potentials admits a global weak solution if the mass, energy and entropy of the initial data are finite. Besides the asymptotic behavior of grazing collisions of the relativistic Boltzmann equation is concerned. We prove that the subsequences of solutions to the relativistic Boltzmann equation weakly converge to the solutions of the relativistic Landau equation when almost all the collisions are grazing. These results are extensions of the work of Villani for the spatially homogeneous Boltzmann and Landau equations in the classical case.Keywords: Relativistic Boltzmann equationrelativistic Landau equationsoft potentialsgrazing collision2010 Mathematics Subject Classification: 35Q20 AcknowledgementsThe authors would like to thank the referees of this paper for their helpful suggestions on this work.Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis work was supported by NSFC 11171356.
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