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Stability and Large-Time Behavior on 3D Incompressible MHD Equations with Partial Dissipation Near a Background Magnetic Field 背景磁场附近部分耗散的三维不可压缩MHD方程的稳定性和大时间行为
IF 2.6 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2025-04-10 DOI: 10.1007/s00205-025-02100-4
Hongxia Lin, Jiahong Wu, Yi Zhu
{"title":"Stability and Large-Time Behavior on 3D Incompressible MHD Equations with Partial Dissipation Near a Background Magnetic Field","authors":"Hongxia Lin,&nbsp;Jiahong Wu,&nbsp;Yi Zhu","doi":"10.1007/s00205-025-02100-4","DOIUrl":"10.1007/s00205-025-02100-4","url":null,"abstract":"<div><p>Physical experiments and numerical simulations have observed a remarkable stabilizing phenomenon: a background magnetic field stabilizes and dampens electrically conducting fluids. This paper intends to establish this phenomenon as a mathematically rigorous fact on a magnetohydrodynamic (MHD) system with anisotropic dissipation in <span>(mathbb R^3)</span>. The velocity equation in this system is the 3D Navier–Stokes equation with dissipation only in the <span>(x_1)</span>-direction, while the magnetic field obeys the induction equation with magnetic diffusion in two horizontal directions. We establish that any perturbation near the background magnetic field (0, 1, 0) is globally stable in the Sobolev setting <span>(H^3({mathbb {R}}^3))</span>. In addition, explicit decay rates in <span>(H^2({mathbb {R}}^3))</span> are also obtained. For when there is no presence of a magnetic field, the 3D anisotropic Navier–Stokes equation is not well understood and the small data global well-posedness in <span>(mathbb R^3)</span> remains an intriguing open problem. This paper reveals the mechanism of how the magnetic field generates enhanced dissipation and helps to stabilize the fluid.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"249 3","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00205-025-02100-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143818214","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Self-Similar Converging Shock Waves 关于自相似收敛激波
IF 2.6 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2025-04-03 DOI: 10.1007/s00205-025-02096-x
Juhi Jang, Jiaqi Liu, Matthew Schrecker
{"title":"On Self-Similar Converging Shock Waves","authors":"Juhi Jang,&nbsp;Jiaqi Liu,&nbsp;Matthew Schrecker","doi":"10.1007/s00205-025-02096-x","DOIUrl":"10.1007/s00205-025-02096-x","url":null,"abstract":"<div><p>In this paper, we rigorously prove the existence of self-similar converging shock wave solutions for the non-isentropic Euler equations for <span>(gamma in (1,3])</span>. These solutions are analytic away from the shock interface before collapse, and the shock wave reaches the origin at the time of collapse. The region behind the shock undergoes a sonic degeneracy, which causes numerous difficulties for smoothness of the flow and the analytic construction of the solution. The proof is based on continuity arguments, nonlinear invariances, and barrier functions.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"249 3","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00205-025-02096-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143769770","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Hydrodynamic Limit of Multiscale Viscoelastic Models for Rigid Particle Suspensions 刚性颗粒悬浮液多尺度粘弹性模型的水动力极限
IF 2.6 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2025-03-20 DOI: 10.1007/s00205-025-02092-1
Mitia Duerinckx, Lucas Ertzbischoff, Alexandre Girodroux-Lavigne, Richard M. Höfer
{"title":"Hydrodynamic Limit of Multiscale Viscoelastic Models for Rigid Particle Suspensions","authors":"Mitia Duerinckx,&nbsp;Lucas Ertzbischoff,&nbsp;Alexandre Girodroux-Lavigne,&nbsp;Richard M. Höfer","doi":"10.1007/s00205-025-02092-1","DOIUrl":"10.1007/s00205-025-02092-1","url":null,"abstract":"<div><p>We study the multiscale viscoelastic Doi model for suspensions of Brownian rigid rod-like particles, as well as its generalization by Saintillan and Shelley for self-propelled particles. We consider the regime of a small Weissenberg number, which corresponds to a fast rotational diffusion compared to the fluid velocity gradient, and we analyze the resulting hydrodynamic approximation. More precisely, we show the asymptotic validity of macroscopic nonlinear viscoelastic models, in form of so-called ordered fluid models, as an expansion in the Weissenberg number. The result holds for zero Reynolds number in 3D and for arbitrary Reynolds number in 2D. Along the way, we establish several new well-posedness and regularity results for nonlinear fluid models, which may be of independent interest.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"249 2","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143668092","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Least Action Admissibility Principle 最小行为可采原则
IF 2.6 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2025-03-09 DOI: 10.1007/s00205-025-02094-z
H. Gimperlein, M. Grinfeld, R. J. Knops, M. Slemrod
{"title":"The Least Action Admissibility Principle","authors":"H. Gimperlein,&nbsp;M. Grinfeld,&nbsp;R. J. Knops,&nbsp;M. Slemrod","doi":"10.1007/s00205-025-02094-z","DOIUrl":"10.1007/s00205-025-02094-z","url":null,"abstract":"<div><p>This paper provides a new admissibility criterion for choosing physically relevant weak solutions of the equations of Lagrangian and continuum mechanics when non-uniqueness of solutions to the initial value problem occurs. The criterion is motivated by the classical least action principle but is now applied to initial value problems which exhibit non-unique solutions. Examples are provided for Lagrangian mechanics and the Euler equations of barotropic fluid mechanics. In particular, we show that the least action admissibility principle prefers the classical two shock solution to the Riemann initial value problem to certain solutions generated by convex integration. On the other hand, Dafermos’s entropy criterion prefers convex integration solutions to the two shock solutions. Furthermore, when the pressure is given by <span>(p(rho )=rho ^2)</span>, we show that the two shock solution is always preferred whenever the convex integration solutions are defined for the same initial data.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"249 2","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143581275","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Conservation Laws for p-Harmonic Systems with Antisymmetric Potentials and Applications 具有反对称势的p-调和系统的守恒定律及其应用
IF 2.6 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2025-03-06 DOI: 10.1007/s00205-025-02085-0
Francesca Da Lio, Tristan Rivière
{"title":"Conservation Laws for p-Harmonic Systems with Antisymmetric Potentials and Applications","authors":"Francesca Da Lio,&nbsp;Tristan Rivière","doi":"10.1007/s00205-025-02085-0","DOIUrl":"10.1007/s00205-025-02085-0","url":null,"abstract":"<div><p>We prove that <i>p</i>-harmonic systems with antisymmetric potentials of the form </p><div><div><span>$$begin{aligned} -,text{ div }left( (1+|nabla u|^2)^{frac{p}{2}-1},nabla uright) =(1+|nabla u|^2)^{frac{p}{2}-1},Omega cdot nabla u, end{aligned}$$</span></div></div><p>(<span>(Omega )</span> is antisymmetric) can be written in divergence form as a conservation law </p><div><div><span>$$begin{aligned} -text{ div }left( (1+|nabla u|^2)^{frac{p}{2}-1},A,nabla uright) =nabla ^perp Bcdot nabla u. end{aligned}$$</span></div></div><p>This extends to the <i>p</i>-harmonic framework the original work of the second author for <span>(p=2)</span> (see Rivière in Invent Math 168(1):1–22, 2007). We give applications of the existence of this divergence structure in the analysis <span>(prightarrow 2)</span>.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"249 2","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00205-025-02085-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143554154","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
BCS Critical Temperature on Half-Spaces 半空间上BCS临界温度
IF 2.6 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2025-03-02 DOI: 10.1007/s00205-025-02088-x
Barbara Roos, Robert Seiringer
{"title":"BCS Critical Temperature on Half-Spaces","authors":"Barbara Roos,&nbsp;Robert Seiringer","doi":"10.1007/s00205-025-02088-x","DOIUrl":"10.1007/s00205-025-02088-x","url":null,"abstract":"<div><p>We study the BCS critical temperature on half-spaces in dimensions <span>(d=1,2,3)</span> with Dirichlet or Neumann boundary conditions. We prove that the critical temperature on a half-space is strictly higher than on <span>(mathbb {R}^d)</span>, at least at weak coupling in <span>(d=1,2)</span> and weak coupling and small chemical potential in <span>(d=3)</span>. Furthermore, we show that the relative shift in critical temperature vanishes in the weak coupling limit.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"249 2","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00205-025-02088-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143529998","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Well-Posedness of Degenerate Initial-Boundary Value Problems to a Hyperbolic-Parabolic Coupled System Arising from Nematic Liquid Crystals 向列液晶双曲-抛物耦合系统退化初边值问题的适定性
IF 2.6 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2025-02-28 DOI: 10.1007/s00205-025-02093-0
Yanbo Hu, Yuusuke Sugiyama
{"title":"Well-Posedness of Degenerate Initial-Boundary Value Problems to a Hyperbolic-Parabolic Coupled System Arising from Nematic Liquid Crystals","authors":"Yanbo Hu,&nbsp;Yuusuke Sugiyama","doi":"10.1007/s00205-025-02093-0","DOIUrl":"10.1007/s00205-025-02093-0","url":null,"abstract":"<div><p>This paper is focused on the local well-posedness of initial-boundary value and Cauchy problems to a one-dimensional quasilinear hyperbolic-parabolic coupled system with boundary or far field degenerate initial data. The governing system is derived from the theory of nematic liquid crystals, which couples a hyperbolic equation describing the crystal property and a parabolic equation describing the liquid property of the material. The hyperbolic equation is degenerate at the boundaries or spatial infinity, which results in the classical methods for the strictly hyperbolic-parabolic coupled systems being invalid. We introduce admissible weighted function spaces and apply the parametrix method to construct iteration mappings for these two degenerate problems separately. The local existence and uniqueness of classical solutions of the degenerate initial-boundary value and Cauchy problems are established by the contraction mapping principle in their selected function spaces. Moreover, the solutions have no loss of regularity and their existence times are independent of the spatial variable.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"249 2","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143513360","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Quantitative Homogenization of State-Constraint Hamilton–Jacobi Equations on Perforated Domains and Applications 穿孔区域上状态约束Hamilton-Jacobi方程的定量均匀化及其应用
IF 2.6 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2025-02-25 DOI: 10.1007/s00205-025-02091-2
Yuxi Han, Wenjia Jing, Hiroyoshi Mitake, Hung V. Tran
{"title":"Quantitative Homogenization of State-Constraint Hamilton–Jacobi Equations on Perforated Domains and Applications","authors":"Yuxi Han,&nbsp;Wenjia Jing,&nbsp;Hiroyoshi Mitake,&nbsp;Hung V. Tran","doi":"10.1007/s00205-025-02091-2","DOIUrl":"10.1007/s00205-025-02091-2","url":null,"abstract":"<div><p>We study the periodic homogenization problem of state-constraint Hamilton–Jacobi equations on perforated domains in the convex setting and obtain the optimal convergence rate. We then consider a dilute situation in which the diameter of the holes is much smaller than the microscopic scale. Finally, a homogenization problem with domain defects where some holes are missing is analyzed.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"249 2","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143489387","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Local Decay Estimates 当地衰减估计值
IF 2.6 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2025-02-13 DOI: 10.1007/s00205-025-02089-w
Avy Soffer, Xiaoxu Wu
{"title":"Local Decay Estimates","authors":"Avy Soffer,&nbsp;Xiaoxu Wu","doi":"10.1007/s00205-025-02089-w","DOIUrl":"10.1007/s00205-025-02089-w","url":null,"abstract":"<div><p>We give a proof of local decay estimates for Schrödinger-type equations, which is based on the knowledge of Asymptotic Completeness. This approach extends to time dependent potential perturbations, as it does not rely on Resolvent Estimates or related methods. Global in time Strichartz estimates follow for quasi-periodic time-dependent potentials from our results.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"249 2","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00205-025-02089-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143396694","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Minimization of the Willmore Energy Under a Constraint on Total Mean Curvature and Area 关于总平均曲率和面积约束下Willmore能量的最小化
IF 2.6 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2025-02-13 DOI: 10.1007/s00205-025-02087-y
Christian Scharrer, Alexander West
{"title":"On the Minimization of the Willmore Energy Under a Constraint on Total Mean Curvature and Area","authors":"Christian Scharrer,&nbsp;Alexander West","doi":"10.1007/s00205-025-02087-y","DOIUrl":"10.1007/s00205-025-02087-y","url":null,"abstract":"<div><p>Motivated by a model for lipid bilayer cell membranes, we study the minimization of the Willmore functional in the class of oriented closed surfaces with prescribed total mean curvature, prescribed area, and prescribed genus. Adapting methods previously developed by Keller–Mondino–Rivière, Bauer–Kuwert, and Ndiaye–Schätzle, we prove the existence of smooth minimizers for a large class of constraints. Moreover, we analyze the asymptotic behaviour of the energy profile close to the unit sphere and consider the total mean curvature of axisymmetric surfaces.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"249 2","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00205-025-02087-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143404265","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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