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Communications on Pure and Applied Mathematics最新文献

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Long range order for random field Ising and Potts models 随机场Ising和Potts模型的长程阶
IF 3 1区 数学
Communications on Pure and Applied Mathematics Pub Date : 2023-07-22 DOI: 10.1002/cpa.22127
Jian Ding, Zijie Zhuang
{"title":"Long range order for random field Ising and Potts models","authors":"Jian Ding,&nbsp;Zijie Zhuang","doi":"10.1002/cpa.22127","DOIUrl":"10.1002/cpa.22127","url":null,"abstract":"<p>We present a new and simple proof for the classic results of Imbrie (1985) and Bricmont–Kupiainen (1988) that for the random field Ising model in dimension three and above there is long range order at low temperatures with presence of weak disorder. With the same method, we obtain a couple of new results: (1) we prove that long range order exists for the random field Potts model at low temperatures with presence of weak disorder in dimension three and above; (2) we obtain a lower bound on the correlation length for the random field Ising model at low temperatures in dimension two (which matches the upper bound in Ding–Wirth (2020)). Our proof is based on an extension of the Peierls argument with inputs from Chalker (1983), Fisher–Fröhlich–Spencer (1984), Ding–Wirth (2020) and Talagrand's majorizing measure theory (1980s) (and in particular, our proof does not involve the renormalization group theory).</p>","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2023-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48635456","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: 9
Large deviations principle for the cubic NLS equation 三次NLS方程的大偏差原理
IF 3 1区 数学
Communications on Pure and Applied Mathematics Pub Date : 2023-07-21 DOI: 10.1002/cpa.22131
Miguel Angel Garrido, Ricardo Grande, Kristin M. Kurianski, Gigliola Staffilani
{"title":"Large deviations principle for the cubic NLS equation","authors":"Miguel Angel Garrido,&nbsp;Ricardo Grande,&nbsp;Kristin M. Kurianski,&nbsp;Gigliola Staffilani","doi":"10.1002/cpa.22131","DOIUrl":"10.1002/cpa.22131","url":null,"abstract":"<p>In this paper, we present a probabilistic study of rare phenomena of the cubic nonlinear Schrödinger equation on the torus in a weakly nonlinear setting. This equation has been used as a model to numerically study the formation of rogue waves in deep sea. Our results are twofold: first, we introduce a notion of criticality and prove a Large Deviations Principle (LDP) for the subcritical and critical cases. Second, we study the most likely initial conditions that lead to the formation of a rogue wave, from a theoretical and numerical point of view. Finally, we propose several open questions for future research.</p>","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2023-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49415427","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: 4
Contact points with integer frequencies in the thin obstacle problem 薄型障碍问题中频率为整数的接触点
IF 3 1区 数学
Communications on Pure and Applied Mathematics Pub Date : 2023-07-21 DOI: 10.1002/cpa.22126
Ovidiu Savin, Hui Yu
{"title":"Contact points with integer frequencies in the thin obstacle problem","authors":"Ovidiu Savin,&nbsp;Hui Yu","doi":"10.1002/cpa.22126","DOIUrl":"10.1002/cpa.22126","url":null,"abstract":"<p>For the thin obstacle problem, we develop a unified approach that leads to rates of convergence to blow-up profiles at contact points with integer frequencies. For these points, we also obtain a stratification result.</p>","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2023-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cpa.22126","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48200462","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: 8
Regularity for convex viscosity solutions of special Lagrangian equation 特殊拉格朗日方程凸粘性解的正则性
IF 3 1区 数学
Communications on Pure and Applied Mathematics Pub Date : 2023-07-21 DOI: 10.1002/cpa.22130
Jingyi Chen, Ravi Shankar, Yu Yuan
{"title":"Regularity for convex viscosity solutions of special Lagrangian equation","authors":"Jingyi Chen,&nbsp;Ravi Shankar,&nbsp;Yu Yuan","doi":"10.1002/cpa.22130","DOIUrl":"https://doi.org/10.1002/cpa.22130","url":null,"abstract":"<p>We establish interior regularity for convex viscosity solutions of the special Lagrangian equation. Our result states that all such solutions are real analytic in the interior of the domain.</p>","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2023-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50139637","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: 12
Uniform boundedness for finite Morse index solutions to supercritical semilinear elliptic equations 超临界椭圆型方程有限Morse指数解的一致有界性
IF 3 1区 数学
Communications on Pure and Applied Mathematics Pub Date : 2023-07-21 DOI: 10.1002/cpa.22132
Alessio Figalli, Yi Ru-Ya Zhang
{"title":"Uniform boundedness for finite Morse index solutions to supercritical semilinear elliptic equations","authors":"Alessio Figalli,&nbsp;Yi Ru-Ya Zhang","doi":"10.1002/cpa.22132","DOIUrl":"10.1002/cpa.22132","url":null,"abstract":"<p>We consider finite Morse index solutions to semilinear elliptic questions, and we investigate their smoothness. It is well-known that: \u0000\u0000 </p>","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2023-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cpa.22132","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49474874","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: 1
Singularities almost always scatter: Regularity results for non-scattering inhomogeneities 奇点几乎总是散射的:非散射非均匀性的规则性结果
IF 3 1区 数学
Communications on Pure and Applied Mathematics Pub Date : 2023-07-17 DOI: 10.1002/cpa.22117
Fioralba Cakoni, Michael S. Vogelius
{"title":"Singularities almost always scatter: Regularity results for non-scattering inhomogeneities","authors":"Fioralba Cakoni,&nbsp;Michael S. Vogelius","doi":"10.1002/cpa.22117","DOIUrl":"10.1002/cpa.22117","url":null,"abstract":"<p>In this paper we examine necessary conditions for an inhomogeneity to be non-scattering, or equivalently, by negation, sufficient conditions for it to be scattering. These conditions are formulated in terms of the regularity of the boundary of the inhomogeneity. We examine broad classes of incident waves in both two and three dimensions. Our analysis is greatly influenced by the analysis carried out by Williams in order to establish that a domain, which does not possess the Pompeiu Property, has a real analytic boundary. That analysis, as well as ours, relies crucially on classical free boundary regularity results due to Kinderlehrer and Nirenberg, and Caffarelli.</p>","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2023-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47738043","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: 16
Short-time existence for the network flow 网络流的短暂存在
IF 3 1区 数学
Communications on Pure and Applied Mathematics Pub Date : 2023-07-13 DOI: 10.1002/cpa.22111
Jorge Lira, Rafe Mazzeo, Alessandra Pluda, Mariel Sáez
{"title":"Short-time existence for the network flow","authors":"Jorge Lira,&nbsp;Rafe Mazzeo,&nbsp;Alessandra Pluda,&nbsp;Mariel Sáez","doi":"10.1002/cpa.22111","DOIUrl":"10.1002/cpa.22111","url":null,"abstract":"<p>This paper contains a new proof of the short-time existence for the flow by curvature of a network of curves in the plane. Appearing initially in metallurgy and as a model for the evolution of grain boundaries, this flow was later treated by Brakke using varifold methods. There is good reason to treat this problem by a direct PDE approach, but doing so requires one to deal with the singular nature of the PDE at the vertices of the network. This was handled in cases of increasing generality by Bronsard-Reitich, Mantegazza-Novaga-Tortorelli and eventually, in the most general case of irregular networks by Ilmanen-Neves-Schulze. Although the present paper proves a result similar to the one in Ilmanen et al., the method here provides substantially more detailed information about how an irregular network “resolves” into a regular one. Either approach relies on the existence of self-similar expanding solutions found in Mazzeo and Saez. As a precursor to the main theorem, we also prove an unexpected regularity result for the mixed Cauchy-Dirichlet boundary problem for the linear heat equation on a manifold with boundary.</p>","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2023-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42866783","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: 8
Global well-posedness for the one-phase Muskat problem 一期Muskat问题的全局适定性
IF 3 1区 数学
Communications on Pure and Applied Mathematics Pub Date : 2023-07-11 DOI: 10.1002/cpa.22124
Hongjie Dong, Francisco Gancedo, Huy Q. Nguyen
{"title":"Global well-posedness for the one-phase Muskat problem","authors":"Hongjie Dong,&nbsp;Francisco Gancedo,&nbsp;Huy Q. Nguyen","doi":"10.1002/cpa.22124","DOIUrl":"10.1002/cpa.22124","url":null,"abstract":"<p>The free boundary problem for a two-dimensional fluid permeating a porous medium is studied. This is known as the one-phase Muskat problem and is mathematically equivalent to the vertical Hele-Shaw problem driven by gravity force. We prove that if the initial free boundary is the graph of a periodic Lipschitz function, then there exists a global-in-time Lipschitz solution in the strong <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msubsup>\u0000 <mi>L</mi>\u0000 <mi>t</mi>\u0000 <mi>∞</mi>\u0000 </msubsup>\u0000 <msubsup>\u0000 <mi>L</mi>\u0000 <mi>x</mi>\u0000 <mn>2</mn>\u0000 </msubsup>\u0000 </mrow>\u0000 <annotation>$L^infty _t L^2_x$</annotation>\u0000 </semantics></math> sense and it is the unique viscosity solution. The proof requires quantitative estimates for layer potentials and pointwise elliptic regularity in Lipschitz domains. This is the first construction of unique global strong solutions for the Muskat problem with initial data of arbitrary size.</p>","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2023-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45524549","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: 11
Long-time correlations for a hard-sphere gas at equilibrium 平衡状态下硬球气体的长时间相关性
IF 3 1区 数学
Communications on Pure and Applied Mathematics Pub Date : 2023-07-09 DOI: 10.1002/cpa.22120
Thierry Bodineau, Isabelle Gallagher, Laure Saint-Raymond, Sergio Simonella
{"title":"Long-time correlations for a hard-sphere gas at equilibrium","authors":"Thierry Bodineau,&nbsp;Isabelle Gallagher,&nbsp;Laure Saint-Raymond,&nbsp;Sergio Simonella","doi":"10.1002/cpa.22120","DOIUrl":"10.1002/cpa.22120","url":null,"abstract":"<p>It has been known since Lanford that the dynamics of a hard-sphere gas is described in the low density limit by the Boltzmann equation, at least for short times. The classical strategy of proof fails for longer times, even close to equilibrium. In this paper, we introduce a weak convergence method coupled with a sampling argument to prove that the covariance of the fluctuation field around equilibrium is governed by the linearized Boltzmann equation globally in time (including in diffusive regimes). This method is much more robust and simpler than the one devised in Bodineau et al which was specific to the 2D case.</p>","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2023-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48424260","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: 6
Generalization of waving-plate theory to multiple interacting swimmers 波浪板理论在多个相互作用游泳运动员中的推广
IF 3 1区 数学
Communications on Pure and Applied Mathematics Pub Date : 2023-07-07 DOI: 10.1002/cpa.22113
Peter J. Baddoo, Nicholas J. Moore, Anand U. Oza, Darren G. Crowdy
{"title":"Generalization of waving-plate theory to multiple interacting swimmers","authors":"Peter J. Baddoo,&nbsp;Nicholas J. Moore,&nbsp;Anand U. Oza,&nbsp;Darren G. Crowdy","doi":"10.1002/cpa.22113","DOIUrl":"10.1002/cpa.22113","url":null,"abstract":"<p>Early research in aerodynamics and biological propulsion was dramatically advanced by the analytical solutions of Theodorsen, von Kármán, Wu and others. While these classical solutions apply only to isolated swimmers, the flow interactions between multiple swimmers are relevant to many practical applications, including the schooling and flocking of animal collectives. In this work, we derive a class of solutions that describe the hydrodynamic interactions between an arbitrary number of swimmers in a two-dimensional inviscid fluid. Our approach is rooted in multiply-connected complex analysis and exploits several recent results. Specifically, the transcendental (Schottky–Klein) prime function serves as the basic building block to construct the appropriate conformal maps and leading-edge-suction functions, which allows us to solve the modified Schwarz problem that arises. As such, our solutions generalize classical thin aerofoil theory, specifically Wu's waving-plate analysis, to the case of multiple swimmers. For the case of a pair of interacting swimmers, we develop an efficient numerical implementation that allows rapid computations of the forces on each swimmer. We investigate flow-mediated equilibria and find excellent agreement between our new solutions and previously reported experimental results. Our solutions recover and unify disparate results in the literature, thereby opening the door for future studies into the interactions between multiple swimmers.</p>","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2023-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43968704","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: 3
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