Journal de Mathematiques Pures et Appliquees最新文献_第6页

Viscosity driven instability of shear flows without boundaries 无边界剪切流黏度驱动的不稳定性

IF 2.1 1区数学

Journal de Mathematiques Pures et Appliquees Pub Date : 2025-04-25 DOI: 10.1016/j.matpur.2025.103724

Hui Li , Weiren Zhao

引用次数: 0

Properties of periodic Dirac–Fock functional and minimizers 周期Dirac-Fock泛函与极小化器的性质

IF 2.1 1区数学

Journal de Mathematiques Pures et Appliquees Pub Date : 2025-04-25 DOI: 10.1016/j.matpur.2025.103719

Isabelle Catto , Long Meng

{"title":"Properties of periodic Dirac–Fock functional and minimizers","authors":"Isabelle Catto , Long Meng","doi":"10.1016/j.matpur.2025.103719","DOIUrl":"10.1016/j.matpur.2025.103719","url":null,"abstract":"<div><div>Existence of minimizers for the Dirac–Fock model for crystals was recently proved by Paturel and Séré and the authors <span><span>[9]</span></span>. In this paper, inspired by Ghimenti and Lewin's result <span><span>[13]</span></span> for the periodic Hartree–Fock model, we prove that the Fermi level of any periodic Dirac–Fock minimizer is either empty or totally filled when <span><math><mfrac><mrow><mi>α</mi></mrow><mrow><mi>c</mi></mrow></mfrac><mo>≤</mo><msub><mrow><mi>C</mi></mrow><mrow><mi>cri</mi></mrow></msub></math></span> and <span><math><mi>α</mi><mo>></mo><mn>0</mn></math></span>. Here <em>c</em> is the speed of light, <em>α</em> is the fine structure constant, and <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>cri</mi></mrow></msub></math></span> is a constant only depending on the number of electrons and on the charge of nuclei per cell. More importantly, we provide an explicit upper bound for <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>cri</mi></mrow></msub></math></span>.</div><div>Our result implies that any minimizer of the periodic Dirac–Fock model is a projector when <span><math><mfrac><mrow><mi>α</mi></mrow><mrow><mi>c</mi></mrow></mfrac><mo>≤</mo><msub><mrow><mi>C</mi></mrow><mrow><mi>cri</mi></mrow></msub></math></span> and <span><math><mi>α</mi><mo>></mo><mn>0</mn></math></span>. In particular, the non-relativistic regime (i.e., <span><math><mi>c</mi><mo>≫</mo><mn>1</mn></math></span>) and the weak coupling regime (i.e., <span><math><mn>0</mn><mo><</mo><mi>α</mi><mo>≪</mo><mn>1</mn></math></span>) are covered.</div><div>The proof is based on a delicate study of a second-order expansion of the periodic Dirac–Fock functional composed with a retraction that was introduced by Séré in <span><span>[24]</span></span> for atoms and molecules and later extended to the case of crystals in <span><span>[9]</span></span>.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"201 ","pages":"Article 103719"},"PeriodicalIF":2.1,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144067943","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

Critical mass phenomena and blow-up behaviors of ground states in stationary second order mean-field games systems with decreasing cost 代价递减的平稳二阶平均场对策系统基态的临界质量现象和爆炸行为

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 基于Finsler几何和各向异性弹性的球面数据沿测地线重建

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 打破陈-利玛窦的平面平衡参数

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 CR矢量场系统的换向子型和李维型

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 无穷维线性控制系统稳定性的频域判据

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 曲线上向量束的对称积和模空间的导出范畴

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 具有（半）非负各向同性曲率的四维梯度里奇孤子

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