{"title":"Reducibility for the linearized two-component intermediate long-wave equation","authors":"Ying Fu , Changzheng Qu , Xiaoping Wu","doi":"10.1016/j.jfa.2025.110832","DOIUrl":"10.1016/j.jfa.2025.110832","url":null,"abstract":"<div><div>In this paper, we study the reducibility of a class of linear operators depending on time quasi-periodically, which arises from linearizing the two-component intermediate long-wave equation at a small amplitude quasi-periodic function, with a Diophantine frequency vector <span><math><mi>ω</mi><mo>∈</mo><msub><mrow><mi>O</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>ν</mi></mrow></msup></math></span>. We prove that there exists a Cantor-like set <span><math><msub><mrow><mi>O</mi></mrow><mrow><mo>∞</mo></mrow></msub><mo>⊂</mo><msub><mrow><mi>O</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> such that for every <span><math><mi>ω</mi><mo>∈</mo><msub><mrow><mi>O</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span>, these operators can be reduced to the ones with constant coefficients by some linear, real, reversibility-preserving and quasi-periodic time-dependent transformations. As a conclusion, the stability of the solutions of the linearized two-component intermediate long-wave equation is obtained. Besides the KAM reducibility transformation, these transformations are obtained from some pseudo-differential operators and the flows of some PDEs. The key difficulty lies in estimating the norms and the upper and lower bounds of the operators related to the integral operator <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>δ</mi></mrow></msub></math></span> due to their complicated structures. To overcome the difficulties, we treat these operators as the principal pseudo-differential operators up to the remainders of lower order and impose some constraints on the parameters.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 7","pages":"Article 110832"},"PeriodicalIF":1.7,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143132611","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Non-existence and multiplicity of positive solutions for Choquard equations with critical combined nonlinearities","authors":"Shiwang Ma","doi":"10.1016/j.jfa.2025.110826","DOIUrl":"10.1016/j.jfa.2025.110826","url":null,"abstract":"<div><div>We study the non-existence and multiplicity of positive solutions of the nonlinear Choquard type equation<span><span><span>(<em>P</em><sub><em>ε</em></sub>)</span><span><math><mo>−</mo><mi>Δ</mi><mi>u</mi><mo>+</mo><mi>ε</mi><mi>u</mi><mo>=</mo><mo>(</mo><msub><mrow><mi>I</mi></mrow><mrow><mi>α</mi></mrow></msub><mo>⁎</mo><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>p</mi></mrow></msup><mo>)</mo><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>p</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>+</mo><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>q</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>,</mo><mspace></mspace><mrow><mi>in</mi></mrow><mspace></mspace><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>,</mo></math></span></span></span> where <span><math><mi>N</mi><mo>≥</mo><mn>3</mn></math></span> is an integer, <span><math><mi>p</mi><mo>∈</mo><mo>(</mo><mfrac><mrow><mi>N</mi><mo>+</mo><mi>α</mi></mrow><mrow><mi>N</mi></mrow></mfrac><mo>,</mo><mfrac><mrow><mi>N</mi><mo>+</mo><mi>α</mi></mrow><mrow><mi>N</mi><mo>−</mo><mn>2</mn></mrow></mfrac><mo>]</mo></math></span>, <span><math><mi>q</mi><mo>∈</mo><mo>(</mo><mn>2</mn><mo>,</mo><mfrac><mrow><mn>2</mn><mi>N</mi></mrow><mrow><mi>N</mi><mo>−</mo><mn>2</mn></mrow></mfrac><mo>]</mo></math></span>, <span><math><msub><mrow><mi>I</mi></mrow><mrow><mi>α</mi></mrow></msub></math></span> is the Riesz potential of order <span><math><mi>α</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mi>N</mi><mo>)</mo></math></span> and <span><math><mi>ε</mi><mo>></mo><mn>0</mn></math></span> is a parameter. We fix one of <span><math><mi>p</mi><mo>,</mo><mi>q</mi></math></span> as a critical exponent (in the sense of Hardy-Littlewood-Sobolev and Sobolev inequalities) and view the others in <span><math><mi>p</mi><mo>,</mo><mi>q</mi><mo>,</mo><mi>ε</mi><mo>,</mo><mi>α</mi></math></span> as parameters, we find regions in the <span><math><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>,</mo><mi>α</mi><mo>,</mo><mi>ε</mi><mo>)</mo></math></span>-parameter space, such that the corresponding equation has no positive ground state or admits multiple positive solutions. This is a counterpart of the Brezis-Nirenberg Conjecture (Brezis and Nirenberg, 1983 <span><span>[7]</span></span>) for nonlocal elliptic equation in the whole space. Particularly, some threshold results for the existence of ground states and some conditions which insure two positive solutions are obtained. These results are quite different in nature from the corresponding local equation with combined powers nonlinearity and reveal the special influence of the nonlocal term. To the best of our knowledge, the only two papers concerning the multiplicity of positive solutions of elliptic equations with critical growth nonlinearity are given by Atkinson and Peletier (1986) <span><span>[5]</span></span> for elliptic equation on a ball and Wei and Wu (2023) <span><span>[40]</span></span> for elliptic equati","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 7","pages":"Article 110826"},"PeriodicalIF":1.7,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143132574","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Stability for the logarithmic Hardy-Littlewood-Sobolev inequality with application to the Keller-Segel equation","authors":"Eric A. Carlen","doi":"10.1016/j.jfa.2024.110818","DOIUrl":"10.1016/j.jfa.2024.110818","url":null,"abstract":"<div><div>We apply a duality method to prove an optimal stability theorem for the logarithmic Hardy-Littlewood-Sobolev inequality, and we apply it to the estimation of the rate of approach to equilibrium for the critical mass Keller-Segel system.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 6","pages":"Article 110818"},"PeriodicalIF":1.7,"publicationDate":"2025-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143128187","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Bismut Einstein metrics on compact complex manifolds","authors":"Yanan Ye","doi":"10.1016/j.jfa.2024.110805","DOIUrl":"10.1016/j.jfa.2024.110805","url":null,"abstract":"<div><div>We prove that, on a compact complex manifold, a Bismut-Einstein metric with a non-zero Einstein constant is indeed Kähler. Meanwhile, a Bismut-Einstein metric with a zero Einstein constant is Bismut-Ricci flat.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 6","pages":"Article 110805"},"PeriodicalIF":1.7,"publicationDate":"2025-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143174941","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Cesàro-type operators on derivative-type Hilbert spaces of analytic functions: The proof of a conjecture","authors":"Qingze Lin , Huayou Xie","doi":"10.1016/j.jfa.2024.110813","DOIUrl":"10.1016/j.jfa.2024.110813","url":null,"abstract":"<div><div>In this paper, we focus on the boundedness and compactness of the Cesàro-type operators<span><span><span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>μ</mi></mrow></msub><mo>(</mo><mi>f</mi><mo>)</mo><mo>(</mo><mi>z</mi><mo>)</mo><mo>:</mo><mo>=</mo><munderover><mo>∑</mo><mrow><mi>n</mi><mo>=</mo><mn>0</mn></mrow><mrow><mo>∞</mo></mrow></munderover><mrow><mo>(</mo><mspace></mspace><munder><mo>∫</mo><mrow><mi>D</mi></mrow></munder><msup><mrow><mi>ω</mi></mrow><mrow><mi>n</mi></mrow></msup><mi>d</mi><mi>μ</mi><mo>(</mo><mi>ω</mi><mo>)</mo><mo>)</mo></mrow><mrow><mo>(</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>n</mi></mrow></munderover><msub><mrow><mi>a</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>)</mo></mrow><msup><mrow><mi>z</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>,</mo><mspace></mspace><mi>z</mi><mo>∈</mo><mi>D</mi><mo>,</mo></math></span></span></span> where <em>μ</em> is a complex Borel measure on the unit disc <span><math><mi>D</mi></math></span>, acting on two derivative-type Hilbert spaces of analytic functions defined in <span><math><mi>D</mi></math></span>, including the derivative Hardy space <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> and the weighted Dirichlet space <span><math><msubsup><mrow><mi>D</mi></mrow><mrow><mi>α</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mspace></mspace><mo>(</mo><mo>−</mo><mn>1</mn><mo><</mo><mi>α</mi><mo><</mo><mo>∞</mo><mo>)</mo></math></span>. As a by-product, we not only prove a conjecture (recently posed by Galanopoulos-Girela-Merchán) about the sufficient conditions for the compactness of <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>μ</mi></mrow></msub></math></span> acting on weighted Bergman space <span><math><msubsup><mrow><mi>A</mi></mrow><mrow><mi>α</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mspace></mspace><mo>(</mo><mo>−</mo><mn>1</mn><mo><</mo><mi>α</mi><mo><</mo><mo>∞</mo><mo>)</mo></math></span>, but also give a complete characterization for the boundedness and compactness of <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>μ</mi></mrow></msub></math></span> between different weighted Bergman spaces. At last, we collect some unresolved problems and issues for further study.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 6","pages":"Article 110813"},"PeriodicalIF":1.7,"publicationDate":"2025-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143174944","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Structure preservation via the Wasserstein distance","authors":"Daniel Bartl , Shahar Mendelson","doi":"10.1016/j.jfa.2024.110810","DOIUrl":"10.1016/j.jfa.2024.110810","url":null,"abstract":"<div><div>We show that under minimal assumptions on a random vector <span><math><mi>X</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span> and with high probability, given <em>m</em> independent copies of <em>X</em>, the coordinate distribution of each vector <span><math><msubsup><mrow><mo>(</mo><mo>〈</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><mi>θ</mi><mo>〉</mo><mo>)</mo></mrow><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>m</mi></mrow></msubsup></math></span> is dictated by the distribution of the true marginal <span><math><mo>〈</mo><mi>X</mi><mo>,</mo><mi>θ</mi><mo>〉</mo></math></span>. Specifically, we show that with high probability,<span><span><span><math><munder><mi>sup</mi><mrow><mi>θ</mi><mo>∈</mo><msup><mrow><mi>S</mi></mrow><mrow><mi>d</mi><mo>−</mo><mn>1</mn></mrow></msup></mrow></munder><mo></mo><msup><mrow><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>m</mi></mrow></mfrac><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>m</mi></mrow></munderover><msup><mrow><mo>|</mo><msup><mrow><mo>〈</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><mi>θ</mi><mo>〉</mo></mrow><mrow><mo>♯</mo></mrow></msup><mo>−</mo><msubsup><mrow><mi>λ</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi>θ</mi></mrow></msubsup><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup><mo>≤</mo><mi>c</mi><msup><mrow><mo>(</mo><mfrac><mrow><mi>d</mi></mrow><mrow><mi>m</mi></mrow></mfrac><mo>)</mo></mrow><mrow><mn>1</mn><mo>/</mo><mn>4</mn></mrow></msup><mo>,</mo></math></span></span></span> where <span><math><msubsup><mrow><mi>λ</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi>θ</mi></mrow></msubsup><mo>=</mo><mi>m</mi><msub><mrow><mo>∫</mo></mrow><mrow><mo>(</mo><mfrac><mrow><mi>i</mi><mo>−</mo><mn>1</mn></mrow><mrow><mi>m</mi></mrow></mfrac><mo>,</mo><mfrac><mrow><mi>i</mi></mrow><mrow><mi>m</mi></mrow></mfrac><mo>]</mo></mrow></msub><msubsup><mrow><mi>F</mi></mrow><mrow><mo>〈</mo><mi>X</mi><mo>,</mo><mi>θ</mi><mo>〉</mo></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msubsup><mo>(</mo><mi>u</mi><mo>)</mo><mspace></mspace><mi>d</mi><mi>u</mi></math></span> and <span><math><msup><mrow><mi>a</mi></mrow><mrow><mo>♯</mo></mrow></msup></math></span> denotes the monotone non-decreasing rearrangement of <em>a</em>. Moreover, this estimate is optimal.</div><div>The proof follows from a sharp estimate on the worst Wasserstein distance between a marginal of <em>X</em> and its empirical counterpart, <span><math><mfrac><mrow><mn>1</mn></mrow><mrow><mi>m</mi></mrow></mfrac><msubsup><mrow><mo>∑</mo></mrow><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>m</mi></mrow></msubsup><msub><mrow><mi>δ</mi></mrow><mrow><mo>〈</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><mi>θ</mi><mo>〉</mo></mrow></msub></math></span>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 7","pages":"Article 110810"},"PeriodicalIF":1.7,"publicationDate":"2025-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143132575","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Unique continuation for Robin problems with non-smooth potentials","authors":"Zongyuan Li","doi":"10.1016/j.jfa.2024.110811","DOIUrl":"10.1016/j.jfa.2024.110811","url":null,"abstract":"<div><div>In this work, we study the unique continuation properties of Robin boundary value problems with Robin potentials <span><math><mi>η</mi><mo>∈</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>d</mi><mo>−</mo><mn>1</mn><mo>+</mo><mi>ε</mi></mrow></msub></math></span>. Our results generalize earlier ones in which <em>η</em> was assumed to be either zero (Neumann problem) or differentiable.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 6","pages":"Article 110811"},"PeriodicalIF":1.7,"publicationDate":"2025-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143174948","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Dirichlet heat kernel estimates for rectilinear stable processes","authors":"Zhen-Qing Chen , Eryan Hu , Guohuan Zhao","doi":"10.1016/j.jfa.2024.110812","DOIUrl":"10.1016/j.jfa.2024.110812","url":null,"abstract":"<div><div>Let <span><math><mi>d</mi><mo>≥</mo><mn>2</mn></math></span>, <span><math><mi>α</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></span>, and <em>X</em> be the rectilinear <em>α</em>-stable process on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>. We first present a geometric characterization of open subset <span><math><mi>D</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span> so that the part process <span><math><msup><mrow><mi>X</mi></mrow><mrow><mi>D</mi></mrow></msup></math></span> of <em>X</em> in <em>D</em> is irreducible. We then study the properties of the transition density functions of <span><math><msup><mrow><mi>X</mi></mrow><mrow><mi>D</mi></mrow></msup></math></span>, including the strict positivity property as well as their sharp two-sided bounds in <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msup></math></span> domains in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>. Our bounds are shown to be sharp for a class of <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msup></math></span> domains.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 6","pages":"Article 110812"},"PeriodicalIF":1.7,"publicationDate":"2025-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143174946","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the weak contractibility of the space of pure states","authors":"Daniel D. Spiegel , Markus J. Pflaum","doi":"10.1016/j.jfa.2024.110809","DOIUrl":"10.1016/j.jfa.2024.110809","url":null,"abstract":"<div><div>We prove that the space <span><math><mi>P</mi><mo>(</mo><mi>A</mi><mo>)</mo></math></span> of pure states of a nonelementary, simple, separable, real rank zero <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-algebra <span><math><mi>A</mi></math></span> has trivial homotopy groups of all orders when <span><math><mi>P</mi><mo>(</mo><mi>A</mi><mo>)</mo></math></span> is equipped with the weak* topology. The convex-valued and finite-dimensional selection theorems of Michael are used to deform a family of pure states via the action of a homotopy of unitaries so that the entire family evaluates to one on a given projection <span><math><mi>P</mi><mo>∈</mo><mi>A</mi></math></span>. Then, the excision theorem of Akemann, Anderson, and Pedersen is used to iterate this deformation for a sequence of projections in <span><math><mi>A</mi></math></span> excising a base point of the family of pure states, thereby contracting the family to the base point. Finally, we compare our weak contractibility result to the spaces of pure states of commutative <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-algebras and rational rotation algebras, and compute the homotopy groups of the latter in terms of the homotopy groups of spheres.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 6","pages":"Article 110809"},"PeriodicalIF":1.7,"publicationDate":"2025-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143174949","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A blow-down mechanism for the Landau-Coulomb equation","authors":"Maria Pia Gualdani , Raphael Winter","doi":"10.1016/j.jfa.2024.110816","DOIUrl":"10.1016/j.jfa.2024.110816","url":null,"abstract":"<div><div>We investigate the Landau-Coulomb equation and show an explicit blow-down mechanism for a family of initial data that are small-scale, supercritical perturbations of a Maxwellian function. We establish global well-posedness and show that the initial bump region will disappear in a time of order one. We prove that the function remains close to an explicit function during the blow-down. As a consequence, our result shows stretched exponential decay in time of the solution towards equilibrium. The key ingredients of our proof are the explicit blow-down function and a novel two-scale linearization in appropriate time-dependent spaces that yields uniform estimates in the perturbation parameter.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 7","pages":"Article 110816"},"PeriodicalIF":1.7,"publicationDate":"2025-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143132577","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
