Journal de Mathematiques Pures et Appliquees最新文献_第7页

Non-uniqueness & inadmissibility of the vanishing viscosity limit of the passive scalar transport equation 被动标量输运方程黏度消失极限的非唯一性和不可容许性

IF 2.1 1区数学

Journal de Mathematiques Pures et Appliquees Pub Date : 2025-02-21 DOI: 10.1016/j.matpur.2025.103685

L. Huysmans , Edriss S. Titi

{"title":"Non-uniqueness & inadmissibility of the vanishing viscosity limit of the passive scalar transport equation","authors":"L. Huysmans , Edriss S. Titi","doi":"10.1016/j.matpur.2025.103685","DOIUrl":"10.1016/j.matpur.2025.103685","url":null,"abstract":"<div><div>We study the vanishing viscosity/diffusivity limit for the transport of a passive scalar <span><math><mi>f</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo><mo>∈</mo><mi>R</mi></math></span> by a bounded, divergence-free vector field <span><math><mi>u</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>. This is described by the Cauchy problem to the PDE <span><math><mfrac><mrow><mo>∂</mo><mi>f</mi></mrow><mrow><mo>∂</mo><mi>t</mi></mrow></mfrac><mo>+</mo><mi>∇</mi><mo>⋅</mo><mo>(</mo><mi>u</mi><mi>f</mi><mo>)</mo><mo>=</mo><mn>0</mn></math></span>, or with viscosity <span><math><mi>ν</mi><mo>></mo><mn>0</mn></math></span>, to the PDE <span><math><mfrac><mrow><mo>∂</mo><mi>f</mi></mrow><mrow><mo>∂</mo><mi>t</mi></mrow></mfrac><mo>+</mo><mi>∇</mi><mo>⋅</mo><mo>(</mo><mi>u</mi><mi>f</mi><mo>)</mo><mo>−</mo><mi>ν</mi><mi>Δ</mi><mi>f</mi><mo>=</mo><mn>0</mn></math></span>. In the first part of this work, we construct a bounded, divergence-free vector field <span><math><mi>u</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo></math></span> for which, for any non-constant initial datum, the viscous solutions along different subsequences of the vanishing viscosity limit converge to different solutions to the inviscid problem. In the second part, we construct another bounded, divergence-free vector field <span><math><mi>u</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo></math></span> for which, for every initial datum, the vanishing viscosity limit of solutions exists, is unique, and converges to an inviscid solution; however, when the initial datum is not constant, this inviscid limit is physically inadmissible due to increasing energy/entropy.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"198 ","pages":"Article 103685"},"PeriodicalIF":2.1,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143534553","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 Wigdersons' approach to the uncertainty principle 论威格森对测不准原理的研究

IF 2.1 1区数学

Journal de Mathematiques Pures et Appliquees Pub Date : 2025-02-21 DOI: 10.1016/j.matpur.2025.103689

Nuno Costa Dias , Franz Luef , João Nuno Prata

引用次数: 0

Cylindrical estimates for the Cheeger constant and applications 契格常数的圆柱形估计及其应用

IF 2.1 1区数学

Journal de Mathematiques Pures et Appliquees Pub Date : 2025-02-01 DOI: 10.1016/j.matpur.2024.103633

Aldo Pratelli , Giorgio Saracco

引用次数: 0

Formation of trapped surfaces in the Einstein-Yang-Mills system 爱因斯坦-杨-米尔斯系统中捕获面的形成

IF 2.1 1区数学

Journal de Mathematiques Pures et Appliquees Pub Date : 2025-02-01 DOI: 10.1016/j.matpur.2025.103661

Nikolaos Athanasiou , Puskar Mondal , Shing-Tung Yau

引用次数: 0

Homogenization of non-autonomous evolution problems for convolution type operators in randomly evolving media 随机演化介质中卷积算子非自治演化问题的均匀化

IF 2.1 1区数学

Journal de Mathematiques Pures et Appliquees Pub Date : 2025-02-01 DOI: 10.1016/j.matpur.2025.103660

A. Piatnitski , E. Zhizhina

引用次数: 0

Local existence of solutions to 3D Prandtl equations with a special structure 具有特殊结构的三维Prandtl方程解的局部存在性

IF 2.1 1区数学

Journal de Mathematiques Pures et Appliquees Pub Date : 2025-02-01 DOI: 10.1016/j.matpur.2025.103670

Yuming Qin , Xiuqing Wang

引用次数: 0

Graph-to-local limit for the nonlocal interaction equation 非局部相互作用方程的图到局部极限

IF 2.1 1区数学

Journal de Mathematiques Pures et Appliquees Pub Date : 2025-02-01 DOI: 10.1016/j.matpur.2025.103663

Antonio Esposito , Georg Heinze , André Schlichting

{"title":"Graph-to-local limit for the nonlocal interaction equation","authors":"Antonio Esposito , Georg Heinze , André Schlichting","doi":"10.1016/j.matpur.2025.103663","DOIUrl":"10.1016/j.matpur.2025.103663","url":null,"abstract":"<div><div>We study a class of nonlocal partial differential equations presenting a tensor-mobility, in space, obtained asymptotically from nonlocal dynamics on localizing infinite graphs. Our strategy relies on the variational structure of both equations, being a Riemannian and Finslerian gradient flow, respectively. More precisely, we prove that weak solutions of the nonlocal interaction equation on graphs converge to weak solutions of the aforementioned class of nonlocal interaction equation with a tensor-mobility in the Euclidean space. This highlights an interesting property of the graph, being a potential space-discretization for the equation under study.</div><div><span>Résumé</span>. Nous étudions une classe d'équations aux dérivées partielles non locales présentant une mobilité tensorielle, dans l'espace, obtenue asymptotiquement à partir de dynamiques non locales sur des graphes infinis localisants. Notre stratégie repose sur la structure variationnelle des deux équations, qui sont respectivement un flot de gradients riemannien et finslérien. Plus précisément, nous prouvons que les solutions faibles de l'équation d'interaction non locale sur les graphes convergent vers des solutions faibles de la classe mentionnée d'équations d'interaction non locales avec une mobilité tensorielle dans l'espace euclidien. Cela met en évidence une propriété intéressante du graphe, à savoir une discrétisation spatiale potentielle pour l'équation étudiée.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"194 ","pages":"Article 103663"},"PeriodicalIF":2.1,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143147016","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

From transient elastic linkages to friction: A complete study of a penalized fourth order equation with delay 从瞬态弹性连杆到摩擦：一个带时滞的惩罚四阶方程的完整研究

IF 2.1 1区数学

Journal de Mathematiques Pures et Appliquees Pub Date : 2025-02-01 DOI: 10.1016/j.matpur.2025.103665

Vuk Milišić , Philippe Souplet

{"title":"From transient elastic linkages to friction: A complete study of a penalized fourth order equation with delay","authors":"Vuk Milišić , Philippe Souplet","doi":"10.1016/j.matpur.2025.103665","DOIUrl":"10.1016/j.matpur.2025.103665","url":null,"abstract":"<div><div><strong>(English)</strong> In this paper we consider a fourth order nonlinear parabolic delayed problem modeling a quasi-instantaneous turn-over of linkages in the context of cell-motility. The model depends on a small parameter <em>ε</em> which represents a typical time scale of the memory effect. We first prove global existence and uniqueness of solutions for <em>ε</em> fixed. This is achieved by combining suitable fixed-point and energy arguments and by uncovering a nonlocal in time, conserved integral quantity. After giving a complete classification of steady states in terms of elliptic functions, we next show that every solution converges to a steady state as <span><math><mi>t</mi><mo>→</mo><mo>∞</mo></math></span>. When <span><math><mi>ε</mi><mo>→</mo><mn>0</mn></math></span>, we then establish convergence results on finite time intervals, showing that the solution tends in a suitable sense towards the solution of a parabolic problem without delay. Moreover, we establish the convergence of energies as <span><math><mi>ε</mi><mo>→</mo><mn>0</mn></math></span>, which enables us to show that, for <em>ε</em> small enough, the <em>ε</em>-dependent problem inherits part of the large time asymptotics of the limiting parabolic problem.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"194 ","pages":"Article 103665"},"PeriodicalIF":2.1,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143146972","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

Approximation and perturbations of stable solutions to a stationary mean field game system 平稳平均场博弈系统稳定解的逼近与摄动

IF 2.1 1区数学

Journal de Mathematiques Pures et Appliquees Pub Date : 2025-02-01 DOI: 10.1016/j.matpur.2025.103666

Jules Berry , Olivier Ley , Francisco J. Silva

引用次数: 0

Bistable pulsating fronts in slowly oscillating one-dimensional environments 缓慢振荡一维环境中的双稳态脉冲锋

IF 2.1 1区数学

Journal de Mathematiques Pures et Appliquees Pub Date : 2025-02-01 DOI: 10.1016/j.matpur.2025.103668

Weiwei Ding , François Hamel , Xing Liang

{"title":"Bistable pulsating fronts in slowly oscillating one-dimensional environments","authors":"Weiwei Ding , François Hamel , Xing Liang","doi":"10.1016/j.matpur.2025.103668","DOIUrl":"10.1016/j.matpur.2025.103668","url":null,"abstract":"<div><div>We consider reaction-diffusion fronts in spatially periodic bistable media with large periods. Whereas the homogenization regime associated with small periods had been well studied for bistable or Fisher-KPP reactions and, in the latter case, a formula for the limit minimal speeds of fronts in media with large periods had also been obtained thanks to the linear formulation of these minimal speeds and their monotonicity with respect to the period, the main remaining open question is concerned with fronts in bistable environments with large periods. In bistable media the unique front speeds are not linearly determined and are not monotone with respect to the spatial period in general, making the analysis of the limit of large periods more intricate. We show in this paper the existence of and an explicit formula for the limit of bistable front speeds as the spatial period goes to infinity. We also prove that the front profiles converge to a family of front profiles associated with spatially homogeneous equations. The main results are based on uniform estimates on the spatial width of the fronts, which themselves use zero number properties and intersection arguments.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"194 ","pages":"Article 103668"},"PeriodicalIF":2.1,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143146796","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