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Hydrodynamic Limit of Multiscale Viscoelastic Models for Rigid Particle Suspensions
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
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
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
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
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
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
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
Minimizers for an Aggregation Model with Attractive–Repulsive Interaction 具有吸引力-反冲性相互作用的聚集模型的最小化模型
IF 2.6 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2025-02-11 DOI: 10.1007/s00205-025-02084-1
Rupert L. Frank, Ryan W. Matzke
{"title":"Minimizers for an Aggregation Model with Attractive–Repulsive Interaction","authors":"Rupert L. Frank,&nbsp;Ryan W. Matzke","doi":"10.1007/s00205-025-02084-1","DOIUrl":"10.1007/s00205-025-02084-1","url":null,"abstract":"<div><p>We solve explicitly a certain minimization problem for probability measures involving an interaction energy that is repulsive at short distances and attractive at large distances. We complement earlier works by showing that in an optimal part of the remaining parameter regime all minimizers are uniform distributions on a surface of a sphere, thus showing concentration on a lower dimensional set. Our method of proof uses convexity estimates on hypergeometric functions.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"249 2","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00205-025-02084-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143388743","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
Minimality of Vortex Solutions to Ginzburg–Landau Type Systems for Gradient Fields in the Unit Ball in Dimension (Nge 4)
IF 2.6 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2025-01-24 DOI: 10.1007/s00205-025-02082-3
Radu Ignat, Mickael Nahon, Luc Nguyen
{"title":"Minimality of Vortex Solutions to Ginzburg–Landau Type Systems for Gradient Fields in the Unit Ball in Dimension (Nge 4)","authors":"Radu Ignat,&nbsp;Mickael Nahon,&nbsp;Luc Nguyen","doi":"10.1007/s00205-025-02082-3","DOIUrl":"10.1007/s00205-025-02082-3","url":null,"abstract":"<div><p>We prove that the degree-one vortex solution is the unique minimizer for the Ginzburg–Landau functional for gradient fields (that is, the Aviles–Giga model) in the unit ball <span>(B^N)</span> in dimension <span>(N ge 4)</span> and with respect to its boundary value. A similar result is also prove in a model for <span>(mathbb {S}^N)</span>-valued maps arising in the theory of micromagnetics. Two methods are presented. The first method is an extension of the analogous technique previously used to treat the unconstrained Ginzburg–Landau functional in dimension <span>(N ge 7)</span>. The second method uses a symmetrization procedure for gradient fields such that the <span>(L^2)</span>-norm is invariant while the <span>(L^p)</span>-norm with <span>(2&lt; p &lt; infty )</span> and the <span>(H^1)</span>-norm are lowered.\u0000</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"249 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00205-025-02082-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143109642","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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