Journal de Mathematiques Pures et Appliquees最新文献

{"title":"Global controllability to harmonic maps of the heat flow from a circle to a sphere","authors":"Jean-Michel Coron ,&nbsp;Shengquan Xiang","doi":"10.1016/j.matpur.2025.103761","DOIUrl":"10.1016/j.matpur.2025.103761","url":null,"abstract":"<div><div>In this paper, we study the controllability and stabilization problems of the harmonic map heat flow from a circle to a sphere. Combining ideas from control theory, heat flow, differential geometry, and asymptotic analysis, we obtain several important properties, such as small-time local controllability, local quantitative rapid stabilization, obstruction to semi-global asymptotic stabilization, and global controllability to geodesics. Surprisingly, due to the geometric feature of the equation we can also prove the small-time global controllability between harmonic maps within the same homotopy class for general compact Riemannian manifold targets, which is to be compared with the analogous but longstanding open problem for nonlinear heat equations.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"204 ","pages":"Article 103761"},"PeriodicalIF":2.1,"publicationDate":"2025-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144491518","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}

{"title":"Spreading properties and forced traveling waves of reaction-diffusion equations in a time-heterogeneous shifting environment","authors":"Lei Zhang ,&nbsp;Xiao-Qiang Zhao","doi":"10.1016/j.matpur.2025.103759","DOIUrl":"10.1016/j.matpur.2025.103759","url":null,"abstract":"<div><div>In this paper, we study the propagation dynamics for a large class of time and space heterogeneous reaction-diffusion equations <span><math><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><msub><mrow><mi>u</mi></mrow><mrow><mi>x</mi><mi>x</mi></mrow></msub><mo>+</mo><mi>u</mi><mi>g</mi><mo>(</mo><mi>x</mi><mo>−</mo><mi>ω</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>,</mo><mi>t</mi><mo>,</mo><mi>u</mi><mo>)</mo></math></span>, where <span><math><mi>ω</mi><mo>(</mo><mi>t</mi><mo>)</mo></math></span> represents the shifting distance, and the nonlinearity <span><math><mi>u</mi><mi>g</mi><mo>(</mo><mi>ξ</mi><mo>,</mo><mi>t</mi><mo>,</mo><mi>u</mi><mo>)</mo></math></span> is asymptotically of KPP type as <span><math><mi>ξ</mi><mo>→</mo><mo>−</mo><mo>∞</mo></math></span> and is negative as <span><math><mi>ξ</mi><mo>→</mo><mo>+</mo><mo>∞</mo></math></span>. Let <span><math><msup><mrow><mi>c</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span> be the spreading speed of the limiting equation <span><math><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><msub><mrow><mi>u</mi></mrow><mrow><mi>x</mi><mi>x</mi></mrow></msub><mo>+</mo><mi>u</mi><mi>g</mi><mo>(</mo><mo>−</mo><mo>∞</mo><mo>,</mo><mi>t</mi><mo>,</mo><mi>u</mi><mo>)</mo></math></span>. Under the assumption that the shifting speed <span><math><msup><mrow><mi>ω</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>(</mo><mi>t</mi><mo>)</mo></math></span> admits a uniform mean <em>c</em>, we show that the solutions with compactly supported initial data go to zero eventually when <span><math><mi>c</mi><mo>≤</mo><mo>−</mo><msup><mrow><mi>c</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>, the leftward spreading speed is <span><math><mo>−</mo><msup><mrow><mi>c</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span> when <span><math><mi>c</mi><mo>&gt;</mo><mo>−</mo><msup><mrow><mi>c</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>, and the rightward spreading speed is <em>c</em> and <span><math><msup><mrow><mi>c</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span> when <span><math><mi>c</mi><mo>∈</mo><mo>(</mo><mo>−</mo><msup><mrow><mi>c</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>,</mo><msup><mrow><mi>c</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>)</mo></math></span> and <span><math><mi>c</mi><mo>≥</mo><msup><mrow><mi>c</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>, respectively. We also establish the existence, uniqueness and nonexistence of the forced traveling wave in terms of the sign of <span><math><mi>c</mi><mo>−</mo><msup><mrow><mi>c</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"203 ","pages":"Article 103759"},"PeriodicalIF":2.1,"publicationDate":"2025-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144322088","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}

{"title":"A Le Potier-type isomorphism twisted with multiplier submodule sheaves","authors":"Yaxiong Liu ,&nbsp;Zhuo Liu ,&nbsp;Hui Yang ,&nbsp;Xiangyu Zhou","doi":"10.1016/j.matpur.2025.103760","DOIUrl":"10.1016/j.matpur.2025.103760","url":null,"abstract":"<div><div>In this paper, we obtain a Le Potier-type isomorphism theorem twisted with multiplier submodule sheaves, which relates a holomorphic vector bundle endowed with a strongly Nakano semi-positive singular Hermitian metric to the tautological line bundle with the induced metric. As applications, we obtain a Kollár-type injectivity theorem, a Nadel-type vanishing theorem, and a singular holomorphic Morse inequality for holomorphic vector bundles and so on.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"202 ","pages":"Article 103760"},"PeriodicalIF":2.1,"publicationDate":"2025-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144313732","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}

{"title":"Stability of background perturbation for Boltzmann equation","authors":"Yu-Chu Lin ,&nbsp;Haitao Wang ,&nbsp;Kung-Chien Wu","doi":"10.1016/j.matpur.2025.103762","DOIUrl":"10.1016/j.matpur.2025.103762","url":null,"abstract":"<div><div>Consider the Boltzmann equation in the perturbation regime. Since the macroscopic quantities in the background global Maxwellian are obtained through measurements, there are typically some errors involved. This paper investigates the effect of background variations on the solution for a given initial perturbation. Our findings demonstrate that the solution changes continuously with variations in the background and provide a sharp time decay estimate of the associated errors. The proof relies on refined estimates for the linearized solution operator and a proper decomposition of the nonlinear solution.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"204 ","pages":"Article 103762"},"PeriodicalIF":2.1,"publicationDate":"2025-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144338507","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}

{"title":"Gradient estimates for the fractional p-Poisson equation","authors":"Verena Bögelein,&nbsp;Frank Duzaar,&nbsp;Naian Liao,&nbsp;Kristian Moring","doi":"10.1016/j.matpur.2025.103764","DOIUrl":"10.1016/j.matpur.2025.103764","url":null,"abstract":"<div><div>We consider local weak solutions to the fractional <em>p</em>-Poisson equation of order <em>s</em>, i.e. <span><math><msup><mrow><mo>(</mo><mo>−</mo><msub><mrow><mi>Δ</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>)</mo></mrow><mrow><mi>s</mi></mrow></msup><mi>u</mi><mo>=</mo><mi>f</mi></math></span>. In the range <span><math><mi>p</mi><mo>&gt;</mo><mn>1</mn></math></span> and <span><math><mi>s</mi><mo>∈</mo><mo>(</mo><mfrac><mrow><mi>p</mi><mo>−</mo><mn>1</mn></mrow><mrow><mi>p</mi></mrow></mfrac><mo>,</mo><mn>1</mn><mo>)</mo></math></span> we prove Calderón &amp; Zygmund type estimates at the gradient level. More precisely, we show for any <span><math><mi>q</mi><mo>&gt;</mo><mn>1</mn></math></span> that<span><span><span><math><mi>f</mi><mo>∈</mo><msubsup><mrow><mi>L</mi></mrow><mrow><mi>loc</mi></mrow><mrow><mfrac><mrow><mi>q</mi><mi>p</mi></mrow><mrow><mi>p</mi><mo>−</mo><mn>1</mn></mrow></mfrac></mrow></msubsup><mspace></mspace><mo>⟹</mo><mspace></mspace><mi>∇</mi><mi>u</mi><mo>∈</mo><msubsup><mrow><mi>L</mi></mrow><mrow><mi>loc</mi></mrow><mrow><mi>q</mi><mi>p</mi></mrow></msubsup><mo>.</mo></math></span></span></span> The qualitative result is accompanied by a local quantitative estimate.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"204 ","pages":"Article 103764"},"PeriodicalIF":2.1,"publicationDate":"2025-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144338508","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}

{"title":"Harmonic analysis in Dunkl settings","authors":"The Anh Bui","doi":"10.1016/j.matpur.2025.103725","DOIUrl":"10.1016/j.matpur.2025.103725","url":null,"abstract":"<div><div>Let <em>L</em> be the Dunkl Laplacian on the Euclidean space <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span> associated with a normalized root <em>R</em> and a multiplicity function <span><math><mi>k</mi><mo>(</mo><mi>ν</mi><mo>)</mo><mo>≥</mo><mn>0</mn><mo>,</mo><mi>ν</mi><mo>∈</mo><mi>R</mi></math></span>. In this paper, we first prove that the Besov and Triebel-Lizorkin spaces associated with the Dunkl Laplacian <em>L</em> are identical to the Besov and Triebel-Lizorkin spaces defined in the space of homogeneous type <span><math><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>,</mo><mo>‖</mo><mo>⋅</mo><mo>‖</mo><mo>,</mo><mi>d</mi><mi>w</mi><mo>)</mo></math></span>, where <span><math><mi>d</mi><mi>w</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><msub><mrow><mo>∏</mo></mrow><mrow><mi>ν</mi><mo>∈</mo><mi>R</mi></mrow></msub><msup><mrow><mo>〈</mo><mi>ν</mi><mo>,</mo><mi>x</mi><mo>〉</mo></mrow><mrow><mi>k</mi><mo>(</mo><mi>ν</mi><mo>)</mo></mrow></msup><mi>d</mi><mi>x</mi></math></span>. Next, consider the Dunkl transform denoted by <span><math><mi>F</mi></math></span>. We introduce the multiplier operator <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>m</mi></mrow></msub></math></span>, defined as <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>m</mi></mrow></msub><mi>f</mi><mo>=</mo><msup><mrow><mi>F</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>(</mo><mi>m</mi><mi>F</mi><mi>f</mi><mo>)</mo></math></span>, where <em>m</em> is a bounded function defined on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span>. Our second aim is to prove multiplier theorems, including the Hörmander multiplier theorem, for <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>m</mi></mrow></msub></math></span> on the Besov and Tribel-Lizorkin spaces in the space of homogeneous type <span><math><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>,</mo><mo>‖</mo><mo>⋅</mo><mo>‖</mo><mo>,</mo><mi>d</mi><mi>w</mi><mo>)</mo></math></span>. Importantly, our findings present novel results, even in the specific case of the Hardy spaces.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"199 ","pages":"Article 103725"},"PeriodicalIF":2.1,"publicationDate":"2025-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143917987","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}

{"title":"Long time behaviour of the solution of Maxwell's equations in dissipative generalized Lorentz materials (II) A modal approach","authors":"Maxence Cassier ,&nbsp;Patrick Joly ,&nbsp;Luis Alejandro Rosas Martínez","doi":"10.1016/j.matpur.2025.103720","DOIUrl":"10.1016/j.matpur.2025.103720","url":null,"abstract":"<div><div>This work concerns the analysis of electromagnetic dispersive media modelled by generalized Lorentz models. More precisely, this paper is the second of two articles dedicated to the long time behaviour of solutions of Maxwell's equations in dissipative Lorentz media, via the decay rate of the electromagnetic energy for the corresponding Cauchy problem. In opposition to the frequency dependent Lyapunov functions approach used in <span><span>[4]</span></span>, we develop a method based on the spectral analysis of the underlying non selfadjoint operator of the model. Although more involved, this approach is closer to physics, as it uses the dispersion relation of the model, and has the advantage to provide more precise and more optimal results, leading to distinguish the notion of weak and strong dissipation.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"201 ","pages":"Article 103720"},"PeriodicalIF":2.1,"publicationDate":"2025-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144117002","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}

{"title":"Almost-everywhere uniqueness of Lagrangian trajectories for 3D Navier–Stokes revisited","authors":"Lucio Galeati","doi":"10.1016/j.matpur.2025.103723","DOIUrl":"10.1016/j.matpur.2025.103723","url":null,"abstract":"<div><div>We show that, for any Leray solution <em>u</em> to the 3D Navier–Stokes equations with <span><math><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>, the associated deterministic and stochastic Lagrangian trajectories are unique for <em>Lebesgue a.e.</em> initial condition. Additionally, if <span><math><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>∈</mo><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup></math></span>, then pathwise uniqueness is established for the stochastic Lagrangian trajectories starting from <em>every</em> initial condition. The result sharpens and extends the original one by Robinson and Sadowski <span><span>[1]</span></span> and is based on rather different techniques. A key role is played by a newly established asymmetric Lusin–Lipschitz property of Leray solutions <em>u</em>, in the framework of (random) Regular Lagrangian flows.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"200 ","pages":"Article 103723"},"PeriodicalIF":2.1,"publicationDate":"2025-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143907562","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}

{"title":"Sticky-reflecting diffusion as a Wasserstein gradient flow","authors":"Jean-Baptiste Casteras ,&nbsp;Léonard Monsaingeon ,&nbsp;Filippo Santambrogio","doi":"10.1016/j.matpur.2025.103721","DOIUrl":"10.1016/j.matpur.2025.103721","url":null,"abstract":"<div><div>In this paper we identify the Fokker-Planck equation for (reflected) Sticky Brownian Motion as a Wasserstein gradient flow in the space of probability measures. The driving functional is the relative entropy with respect to a non-standard reference measure, the sum of an absolutely continuous interior part plus a singular part supported on the boundary. Taking the small time-step limit in a minimizing movement (JKO scheme) we prove existence of weak solutions for the coupled system of PDEs satisfying in addition an Energy Dissipation Inequality.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"199 ","pages":"Article 103721"},"PeriodicalIF":2.1,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143906987","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}

{"title":"An explicit Euler method for Sobolev vector fields with applications to the continuity equation on non Cartesian grids","authors":"Tommaso Cortopassi","doi":"10.1016/j.matpur.2025.103722","DOIUrl":"10.1016/j.matpur.2025.103722","url":null,"abstract":"<div><div>We prove a novel stability estimate in <span><math><msubsup><mrow><mi>L</mi></mrow><mrow><mi>t</mi></mrow><mrow><mo>∞</mo></mrow></msubsup><mo>(</mo><msubsup><mrow><mi>L</mi></mrow><mrow><mi>x</mi></mrow><mrow><mi>p</mi></mrow></msubsup><mo>)</mo></math></span> between the regular Lagrangian flow of a Sobolev vector field and a piecewise affine approximation of such flow. This approximation of the flow is obtained by a (sort of) explicit Euler method, and it is the crucial tool to prove approximation results for the solution of the continuity equation by using the representation of the solution as the push-forward via the regular Lagrangian flow of the initial datum. We approximate the solution in two ways, using different approximations for both the flow and the initial datum. In the first case we give an estimate, which however holds only in probability, of the Wasserstein distance between the solution of the continuity equation and a discrete approximation of such solution. The approximate solution is defined as the push-forward of weighted Dirac deltas (whose centers are chosen in a probabilistic way). In the second case we give a deterministic estimate of the Wasserstein distance using a slightly different approximation of the regular Lagrangian flow and requiring more regularity on the velocity field <em>u</em> than in the previous case. An advantage of both approximations is that they provide an algorithm which is easily parallelizable and does not rely on any particular structure of the mesh with which we discretize (only in space) the domain. We also compare our estimates to similar ones previously obtained in <span><span>[27]</span></span>, and we show how under certain hypotheses our method provides better convergence rates.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"199 ","pages":"Article 103722"},"PeriodicalIF":2.1,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143906988","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}