Journal de Mathematiques Pures et Appliquees最新文献

Critical mass phenomena and blow-up behaviors of ground states in stationary second order mean-field games systems with decreasing cost

IF 2.1 1区数学

Journal de Mathematiques Pures et Appliquees Pub Date : 2025-02-25 DOI: 10.1016/j.matpur.2025.103687

Marco Cirant , Fanze Kong , Juncheng Wei , Xiaoyu Zeng

{"title":"Critical mass phenomena and blow-up behaviors of ground states in stationary second order mean-field games systems with decreasing cost","authors":"Marco Cirant , Fanze Kong , Juncheng Wei , Xiaoyu Zeng","doi":"10.1016/j.matpur.2025.103687","DOIUrl":"10.1016/j.matpur.2025.103687","url":null,"abstract":"<div><div>This paper is devoted to the study of Mean-field Games (MFG) systems in the mass-critical exponent case. We first derive the optimal Gagliardo-Nirenberg type inequality associated with the potential-free MFG system. Then, under some mild assumptions on the potential function, we show that there exists a critical mass <span><math><msup><mrow><mi>M</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span> such that the MFG system admits a least-energy solution if and only if the total mass of population density <em>M</em> satisfies <span><math><mi>M</mi><mo><</mo><msup><mrow><mi>M</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>. Moreover, the blow-up behavior of energy minimizers is characterized as <span><math><mi>M</mi><mo>↗</mo><msup><mrow><mi>M</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>. In particular, by considering the precise asymptotic expansions of the potential, we establish the refined blow-up behavior of ground states as <span><math><mi>M</mi><mo>↗</mo><msup><mrow><mi>M</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>. While studying the existence of least-energy solutions, we establish new local <span><math><msup><mrow><mi>W</mi></mrow><mrow><mn>2</mn><mo>,</mo><mi>p</mi></mrow></msup></math></span> estimates for solutions to Hamilton-Jacobi equations with superlinear gradient terms.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"198 ","pages":"Article 103687"},"PeriodicalIF":2.1,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143534554","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

Reconstruction along a geodesic from sphere data in Finsler geometry and anisotropic elasticity

IF 2.1 1区数学

Journal de Mathematiques Pures et Appliquees Pub Date : 2025-02-24 DOI: 10.1016/j.matpur.2025.103688

Maarten V. de Hoop , Joonas Ilmavirta , Matti Lassas

引用次数: 0

Blowing up Chern-Ricci flat balanced metrics

IF 2.1 1区数学

Journal de Mathematiques Pures et Appliquees Pub Date : 2025-02-24 DOI: 10.1016/j.matpur.2025.103691

Elia Fusi , Federico Giusti

引用次数: 0

Commutator type and Levi type of a system of CR vector fields

IF 2.1 1区数学

Journal de Mathematiques Pures et Appliquees Pub Date : 2025-02-24 DOI: 10.1016/j.matpur.2025.103693

Xiaojun Huang , Wanke Yin

引用次数: 0

Frequency-domain criterion on the stabilizability for infinite-dimensional linear control systems

IF 2.1 1区数学

Journal de Mathematiques Pures et Appliquees Pub Date : 2025-02-24 DOI: 10.1016/j.matpur.2025.103690

Karl Kunisch , Gengsheng Wang , Huaiqiang Yu

引用次数: 0

Derived categories of symmetric products and moduli spaces of vector bundles on a curve

IF 2.1 1区数学

Journal de Mathematiques Pures et Appliquees Pub Date : 2025-02-24 DOI: 10.1016/j.matpur.2025.103694

Kyoung-Seog Lee , Han-Bom Moon

引用次数: 0

Damping for fractional wave equations and applications to water waves 分数波方程的阻尼及其在水波中的应用

IF 2.1 1区数学

Journal de Mathematiques Pures et Appliquees Pub Date : 2025-02-24 DOI: 10.1016/j.matpur.2025.103692

Thomas Alazard , Jeremy L. Marzuola , Jian Wang

引用次数: 0

Four-dimensional gradient Ricci solitons with (half) nonnegative isotropic curvature

IF 2.1 1区数学

Journal de Mathematiques Pures et Appliquees Pub Date : 2025-02-24 DOI: 10.1016/j.matpur.2025.103686

Huai-Dong Cao , Junming Xie

{"title":"Four-dimensional gradient Ricci solitons with (half) nonnegative isotropic curvature","authors":"Huai-Dong Cao , Junming Xie","doi":"10.1016/j.matpur.2025.103686","DOIUrl":"10.1016/j.matpur.2025.103686","url":null,"abstract":"<div><div>This is a sequel to our paper <span><span>[24]</span></span>, in which we investigated the geometry of 4-dimensional gradient shrinking Ricci solitons with half positive (nonnegative) isotropic curvature. In this paper, we mainly focus on 4-dimensional gradient steady Ricci solitons with nonnegative isotropic curvature (WPIC) or half nonnegative isotropic curvature (half WPIC). In particular, for 4D complete <em>ancient solutions</em> with WPIC, we are able to prove the 2-nonnegativity of the Ricci curvature and bound the curvature tensor <em>Rm</em> by <span><math><mo>|</mo><mi>R</mi><mi>m</mi><mo>|</mo><mo>≤</mo><mi>R</mi></math></span>. For 4D gradient steady solitons with WPIC, we obtain a classification result. We also give a partial classification of 4D gradient steady Ricci solitons with half WPIC. Moreover, we obtain a preliminary classification result for 4D complete gradient <em>expanding Ricci solitons</em> with WPIC. Finally, motivated by the recent work <span><span>[59]</span></span>, we improve our earlier results in <span><span>[24]</span></span> on 4D gradient <em>shrinking Ricci solitons</em> with half PIC or half WPIC, and also provide a characterization of complete gradient Kähler-Ricci shrinkers in complex dimension two among 4-dimensional gradient Ricci shrinkers.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"197 ","pages":"Article 103686"},"PeriodicalIF":2.1,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143511264","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

On Wigdersons' approach to the uncertainty principle

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

Non-uniqueness & inadmissibility of the vanishing viscosity limit of the passive scalar transport equation

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