Communications on Pure and Applied Mathematics最新文献

{"title":"On the Pólya conjecture for the Neumann problem in planar convex domains","authors":"N. Filonov","doi":"10.1002/cpa.22231","DOIUrl":"https://doi.org/10.1002/cpa.22231","url":null,"abstract":"Denote by the counting function of the spectrum of the Neumann problem in the domain on the plane. G. Pólya conjectured that . We prove that for convex domains . Here is the first zero of the Bessel function .","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":"10 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142405396","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":"Smooth asymptotics for collapsing Calabi–Yau metrics","authors":"Hans-Joachim Hein,&nbsp;Valentino Tosatti","doi":"10.1002/cpa.22228","DOIUrl":"10.1002/cpa.22228","url":null,"abstract":"<p>We prove that Calabi–Yau metrics on compact Calabi–Yau manifolds whose Kähler classes shrink the fibers of a holomorphic fibration have a priori estimates of all orders away from the singular fibers. To this end, we prove an asymptotic expansion of these metrics in terms of powers of the fiber diameter, with <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 <mtext>th</mtext>\u0000 </mrow>\u0000 <annotation>$ktext{th}$</annotation>\u0000 </semantics></math>-order remainders that satisfy uniform <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mi>k</mi>\u0000 </msup>\u0000 <annotation>$C^k$</annotation>\u0000 </semantics></math>-estimates with respect to a collapsing family of background metrics. The constants in these estimates are uniform not only in the sense that they are independent of the fiber diameter, but also in the sense that they only depend on the constant in the estimate for <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 <mo>=</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$k = 0$</annotation>\u0000 </semantics></math> known from previous work of the second-named author. For <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 <mo>&gt;</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$k &gt; 0$</annotation>\u0000 </semantics></math>, the new estimates are proved by blowup and contradiction, and each additional term of the expansion arises as the obstruction to proving a uniform bound on one additional derivative of the remainder.</p>","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":"78 2","pages":"382-499"},"PeriodicalIF":3.1,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142397713","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":"Uniqueness of the blow-down limit for a triple junction problem","authors":"Zhiyuan Geng","doi":"10.1002/cpa.22230","DOIUrl":"10.1002/cpa.22230","url":null,"abstract":"<p>We prove the uniqueness of <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 <annotation>$L^1$</annotation>\u0000 </semantics></math> blow-down limit at infinity for an entire minimizing solution <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>u</mi>\u0000 <mo>:</mo>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <mo>→</mo>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$u:mathbb {R}^2rightarrow mathbb {R}^2$</annotation>\u0000 </semantics></math> of a planar Allen–Cahn system with a triple-well potential. Consequently, <span></span><math>\u0000 <semantics>\u0000 <mi>u</mi>\u0000 <annotation>$u$</annotation>\u0000 </semantics></math> can be approximated by a triple junction map at infinity. The proof exploits a careful analysis of energy upper and lower bounds, ensuring that the diffuse interface remains within a small neighborhood of the approximated triple junction at all scales.</p>","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":"78 2","pages":"500-534"},"PeriodicalIF":3.1,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cpa.22230","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142397712","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}

{"title":"Integral formulation of Klein–Gordon singular waveguides","authors":"Guillaume Bal,&nbsp;Jeremy Hoskins,&nbsp;Solomon Quinn,&nbsp;Manas Rachh","doi":"10.1002/cpa.22227","DOIUrl":"10.1002/cpa.22227","url":null,"abstract":"<p>We consider the analysis of singular waveguides separating insulating phases in two-space dimensions. The insulating domains are modeled by a massive Schrödinger equation and the singular waveguide by appropriate jump conditions along the one-dimensional interface separating the insulators. We present an integral formulation of the problem and analyze its mathematical properties. We also implement a fast multipole and sweeping-accelerated iterative algorithm for solving the integral equations, and demonstrate numerically the fast convergence of this method. Several numerical examples of solutions and scattering effects illustrate our theory.</p>","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":"78 2","pages":"323-365"},"PeriodicalIF":3.1,"publicationDate":"2024-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cpa.22227","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142384201","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}

{"title":"On minimizers in the liquid drop model","authors":"Otis Chodosh,&nbsp;Ian Ruohoniemi","doi":"10.1002/cpa.22229","DOIUrl":"10.1002/cpa.22229","url":null,"abstract":"<p>We prove that round balls of volume <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>≤</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$le 1$</annotation>\u0000 </semantics></math> uniquely minimize in Gamow's liquid drop model.</p>","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":"78 2","pages":"366-381"},"PeriodicalIF":3.1,"publicationDate":"2024-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142384202","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":"On the wave turbulence theory of 2D gravity waves, I: Deterministic energy estimates","authors":"Yu Deng,&nbsp;Alexandru D. Ionescu,&nbsp;Fabio Pusateri","doi":"10.1002/cpa.22224","DOIUrl":"10.1002/cpa.22224","url":null,"abstract":"&lt;p&gt;Our goal in this paper is to initiate the rigorous investigation of wave turbulence and derivation of wave kinetic equations (WKEs) for water waves models. This problem has received intense attention in recent years in the context of semilinear models, such as Schrödinger equations or multidimensional KdV-type equations. However, our situation here is different since the water waves equations are quasilinear and solutions cannot be constructed by iteration of the Duhamel formula due to unavoidable derivative loss. This is the first of two papers in which we design a new strategy to address this issue. We investigate solutions of the gravity water waves system in two dimensions. In the irrotational case, this system can be reduced to an evolution equation on the one-dimensional interface, which is a large torus &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;T&lt;/mi&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;${mathbb {T}}_R$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; of size &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;mo&gt;≥&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$Rge 1$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. Our first main result is a deterministic energy inequality, which provides control of (possibly large) Sobolev norms of solutions for long times, under the condition that a certain &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;mi&gt;∞&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;annotation&gt;$L^infty$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-type norm is small. This energy inequality is of “quintic” type: if the &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;mi&gt;∞&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;annotation&gt;$L^infty$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; norm is &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;O&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;ε&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$O(varepsilon)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, then the increment of the high-order energies is controlled for times of the order &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;ε&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mn&gt;3&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;annotation&gt;$varepsilon ^{-3}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, consistent with the approximate quartic integrability of the system. In the second paper in this sequence, we","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":"78 2","pages":"211-322"},"PeriodicalIF":3.1,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cpa.22224","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142170872","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}

{"title":"Convergence to the planar interface for a nonlocal free-boundary evolution","authors":"Felix Otto,&nbsp;Richard Schubert,&nbsp;Maria G. Westdickenberg","doi":"10.1002/cpa.22225","DOIUrl":"10.1002/cpa.22225","url":null,"abstract":"<p>We capture optimal decay for the Mullins–Sekerka evolution, a nonlocal, parabolic free boundary problem from materials science. Our main result establishes convergence of BV solutions to the planar profile in the physically relevant case of ambient space dimension three. Far from assuming small or well-prepared initial data, we allow for initial interfaces that do not have graph structure and are not connected, hence explicitly including the regime of Ostwald ripening. In terms only of initially finite (not small) excess mass and excess surface energy, we establish that the surface becomes a Lipschitz graph within a fixed timescale (quantitatively estimated) and remains trapped within this setting. To obtain the graph structure, we leverage regularity results from geometric measure theory. At the same time, we extend a duality method previously employed for one-dimensional PDE problems to higher dimensional, nonlocal geometric evolutions. Optimal algebraic decay rates of excess energy, dissipation, and graph height are obtained.</p>","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":"78 1","pages":"161-208"},"PeriodicalIF":3.1,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cpa.22225","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142142410","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}

{"title":"Asymptotics of block Toeplitz determinants with piecewise continuous symbols","authors":"Estelle Basor,&nbsp;Torsten Ehrhardt,&nbsp;Jani A. Virtanen","doi":"10.1002/cpa.22223","DOIUrl":"10.1002/cpa.22223","url":null,"abstract":"<p>We determine the asymptotics of the block Toeplitz determinants <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>det</mo>\u0000 <msub>\u0000 <mi>T</mi>\u0000 <mi>n</mi>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>ϕ</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$det T_n(phi)$</annotation>\u0000 </semantics></math> as <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>→</mo>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 <annotation>$nrightarrow infty$</annotation>\u0000 </semantics></math> for <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>N</mi>\u0000 <mo>×</mo>\u0000 <mi>N</mi>\u0000 </mrow>\u0000 <annotation>$Ntimes N$</annotation>\u0000 </semantics></math> matrix-valued piecewise continuous functions <span></span><math>\u0000 <semantics>\u0000 <mi>ϕ</mi>\u0000 <annotation>$phi$</annotation>\u0000 </semantics></math> with a finitely many jumps under mild additional conditions. In particular, we prove that\u0000\u0000 </p>","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":"78 1","pages":"120-160"},"PeriodicalIF":3.1,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cpa.22223","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142090102","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}

{"title":"Tight Lipschitz hardness for optimizing mean field spin glasses","authors":"Brice Huang,&nbsp;Mark Sellke","doi":"10.1002/cpa.22222","DOIUrl":"https://doi.org/10.1002/cpa.22222","url":null,"abstract":"&lt;p&gt;We study the problem of algorithmically optimizing the Hamiltonian &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;mi&gt;N&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$H_N$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; of a spherical or Ising mixed &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;annotation&gt;$p$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-spin glass. The maximum asymptotic value &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;OPT&lt;/mi&gt;\u0000 &lt;annotation&gt;${mathsf {OPT}}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;mi&gt;N&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;mi&gt;N&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$H_N/N$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is characterized by a variational principle known as the Parisi formula, proved first by Talagrand and in more generality by Panchenko. Recently developed approximate message passing (AMP) algorithms efficiently optimize &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;mi&gt;N&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;mi&gt;N&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$H_N/N$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; up to a value &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;ALG&lt;/mi&gt;\u0000 &lt;annotation&gt;${mathsf {ALG}}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; given by an extended Parisi formula, which minimizes over a larger space of functional order parameters. These two objectives are equal for spin glasses exhibiting a &lt;i&gt;no overlap gap&lt;/i&gt; property (OGP). However, &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ALG&lt;/mi&gt;\u0000 &lt;mo&gt;&lt;&lt;/mo&gt;\u0000 &lt;mi&gt;OPT&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;${mathsf {ALG}}&amp;lt; {mathsf {OPT}}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; can also occur, and no efficient algorithm producing an objective value exceeding &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;ALG&lt;/mi&gt;\u0000 &lt;annotation&gt;${mathsf {ALG}}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is known. We prove that for mixed even &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;annotation&gt;$p$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-spin models, no algorithm satisfying an &lt;i&gt;overlap concentration&lt;/i&gt; property can produce an objective larger than &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;ALG&lt;/mi&gt;\u0000 &lt;annotation&gt;${mathsf {ALG}}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; with non-negligible probability.","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":"78 1","pages":"60-119"},"PeriodicalIF":3.1,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142665074","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":"Global regularity for critical SQG in bounded domains","authors":"Peter Constantin,&nbsp;Mihaela Ignatova,&nbsp;Quoc-Hung Nguyen","doi":"10.1002/cpa.22221","DOIUrl":"10.1002/cpa.22221","url":null,"abstract":"<p>We prove the existence and uniqueness of global smooth solutions of the critical dissipative SQG equation in bounded domains in <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <annotation>$mathbb {R}^2$</annotation>\u0000 </semantics></math>. We introduce a new methodology of transforming the single nonlocal nonlinear evolution equation in a bounded domain into an interacting system of extended nonlocal nonlinear evolution equations in the whole space. The proof then uses the method of the nonlinear maximum principle for nonlocal operators in the extended system.</p>","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":"78 1","pages":"3-59"},"PeriodicalIF":3.1,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141755298","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}