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Communications in Partial Differential Equations最新文献

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Reversed Strichartz estimates for wave on non-trapping asymptotically hyperbolic manifolds and applications 非陷波渐近双曲流形上波的逆Strichartz估计及其应用
IF 1.9 2区 数学
Communications in Partial Differential Equations Pub Date : 2021-08-26 DOI: 10.1080/03605302.2022.2047724
Y. Sire, C. Sogge, Chengbo Wang, Junyong Zhang
{"title":"Reversed Strichartz estimates for wave on non-trapping asymptotically hyperbolic manifolds and applications","authors":"Y. Sire, C. Sogge, Chengbo Wang, Junyong Zhang","doi":"10.1080/03605302.2022.2047724","DOIUrl":"https://doi.org/10.1080/03605302.2022.2047724","url":null,"abstract":"Abstract We provide reversed Strichartz estimates for the shifted wave equations on non-trapping asymptotically hyperbolic manifolds using cluster estimates for spectral projectors proved previously in such generality. As a consequence, we solve a problem left open in Sire et al [Trans. AMS 373(2020):7639-7668] about the endpoint case for global well-posedness of nonlinear wave equations. We also provide estimates in this context for the maximal wave operator.","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2021-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45866369","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}
引用次数: 4
Hamilton–Jacobi equations with their Hamiltonians depending Lipschitz continuously on the unknown Hamilton–Jacobi方程及其哈密顿量连续依赖于未知的Lipschitz
IF 1.9 2区 数学
Communications in Partial Differential Equations Pub Date : 2021-08-25 DOI: 10.1080/03605302.2021.1983598
H. Ishii, Kaizhi Wang, Lin Wang, Jun Yan
{"title":"Hamilton–Jacobi equations with their Hamiltonians depending Lipschitz continuously on the unknown","authors":"H. Ishii, Kaizhi Wang, Lin Wang, Jun Yan","doi":"10.1080/03605302.2021.1983598","DOIUrl":"https://doi.org/10.1080/03605302.2021.1983598","url":null,"abstract":"Abstract We study the Hamilton–Jacobi equations in M and in where the Hamiltonian depends Lipschitz continuously on the variable u. In the framework of the semicontinuous viscosity solutions due to Barron–Jensen, we establish the comparison principle, existence theorem, and representation formula as value functions for extended real-valued, lower semicontinuous solutions for the Cauchy problem. We also establish some results on the long-time behavior of solutions for the Cauchy problem and classification of solutions for the stationary problem.","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2021-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43956121","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}
引用次数: 4
Critical points of Laplace eigenfunctions on polygons 多边形上拉普拉斯特征函数的临界点
IF 1.9 2区 数学
Communications in Partial Differential Equations Pub Date : 2021-08-23 DOI: 10.1080/03605302.2022.2062572
C. Judge, Sugata Mondal
{"title":"Critical points of Laplace eigenfunctions on polygons","authors":"C. Judge, Sugata Mondal","doi":"10.1080/03605302.2022.2062572","DOIUrl":"https://doi.org/10.1080/03605302.2022.2062572","url":null,"abstract":"Abstract We study the critical points of Laplace eigenfunctions on polygonal domains with a focus on the second Neumann eigenfunction. We show that if each convex quadrilaterals has no second Neumann eigenfunction with an interior critical point, then there exists a convex quadrilateral with an unstable critical point. We also show that each critical point of a second-Neumann eigenfunction on a Lip-1 polygon with no orthogonal sides is an acute vertex.","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2021-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47703514","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}
引用次数: 3
Sticky particle Cucker–Smale dynamics and the entropic selection principle for the 1D Euler-alignment system 一维欧拉对准系统的粘性粒子cucker -小动力学和熵选择原理
IF 1.9 2区 数学
Communications in Partial Differential Equations Pub Date : 2021-08-17 DOI: 10.1080/03605302.2023.2202720
T. Leslie, Changhui Tan
{"title":"Sticky particle Cucker–Smale dynamics and the entropic selection principle for the 1D Euler-alignment system","authors":"T. Leslie, Changhui Tan","doi":"10.1080/03605302.2023.2202720","DOIUrl":"https://doi.org/10.1080/03605302.2023.2202720","url":null,"abstract":"Abstract We develop a global wellposedness theory for weak solutions to the 1D Euler-alignment system with measure-valued density, bounded velocity, and locally integrable communication protocol. A satisfactory understanding of the low-regularity theory is an issue of pressing interest, as smooth solutions may lose regularity in finite time. However, no such theory currently exists except for a very special class of alignment interactions. We show that the dynamics of the 1D Euler-alignment system can be effectively described by a nonlocal scalar balance law, the entropy conditions of which serves as an entropic selection principle that determines a unique weak solution of the Euler-alignment system. Moreover, the distinguished weak solution of the system can be approximated by the sticky particle Cucker–Smale dynamics. Our approach is inspired by the work of Brenier and Grenier on the pressureless Euler equations.","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2021-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44876221","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}
引用次数: 5
The streamlines of ∞-harmonic functions obey the inverse mean curvature flow ∞-调和函数的流线服从逆平均曲率流
IF 1.9 2区 数学
Communications in Partial Differential Equations Pub Date : 2021-08-12 DOI: 10.1080/03605302.2022.2109487
R. Moser
{"title":"The streamlines of ∞-harmonic functions obey the inverse mean curvature flow","authors":"R. Moser","doi":"10.1080/03605302.2022.2109487","DOIUrl":"https://doi.org/10.1080/03605302.2022.2109487","url":null,"abstract":"Abstract Given an ∞-harmonic function on a domain consider the function If with and then it is easy to check that the streamlines of are the level sets of w and w solves the level set formulation of the inverse mean curvature flow. For less regular solutions, neither statement is true in general, but even so, w is still a weak solution of the inverse mean curvature flow under far weaker assumptions. This is proved through an approximation of by p-harmonic functions, the use of conjugate -harmonic functions, and the known connection of the latter with the inverse mean curvature flow. A statement about the regularity of arises as a by-product.","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2021-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45863210","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}
引用次数: 0
Nonuniqueness and nonlinear instability of Gaussons under repulsive harmonic potential 排斥谐波势下高斯子的非唯一性和非线性不稳定性
IF 1.9 2区 数学
Communications in Partial Differential Equations Pub Date : 2021-07-21 DOI: 10.1080/03605302.2022.2050257
R. Carles, Chunmei Su
{"title":"Nonuniqueness and nonlinear instability of Gaussons under repulsive harmonic potential","authors":"R. Carles, Chunmei Su","doi":"10.1080/03605302.2022.2050257","DOIUrl":"https://doi.org/10.1080/03605302.2022.2050257","url":null,"abstract":"Abstract We consider the Schrödinger equation with a nondispersive logarithmic nonlinearity and a repulsive harmonic potential. For a suitable range of the coefficients, there exist two positive stationary solutions, each one generating a continuous family of solitary waves. These solutions are Gaussian, and turn out to be orbitally unstable. We also discuss the notion of ground state in this setting: for any natural definition, the set of ground states is empty.","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2021-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48368245","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}
引用次数: 5
Filamentation near Hill’s vortex 希尔涡旋附近的细丝化
IF 1.9 2区 数学
Communications in Partial Differential Equations Pub Date : 2021-07-13 DOI: 10.1080/03605302.2022.2139721
Kyudong Choi, In-Jee Jeong
{"title":"Filamentation near Hill’s vortex","authors":"Kyudong Choi, In-Jee Jeong","doi":"10.1080/03605302.2022.2139721","DOIUrl":"https://doi.org/10.1080/03605302.2022.2139721","url":null,"abstract":"Abstract For the axi-symmetric incompressible Euler equations, we prove linear in time filamentation near Hill’s vortex: there exists an arbitrary small outward perturbation growing linearly for all times. This is based on combining the recent nonlinear orbital stability obtained by the first author with a dynamical bootstrapping scheme for particle trajectories. These results rigorously confirm numerical simulations by Pozrikidis in 1986.","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2021-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47241067","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}
引用次数: 8
Global Strichartz estimates for an inhomogeneous Maxwell system 非均匀Maxwell系统的全局Strichartz估计
IF 1.9 2区 数学
Communications in Partial Differential Equations Pub Date : 2021-06-30 DOI: 10.1080/03605302.2021.1998910
P. D’Ancona, R. Schnaubelt
{"title":"Global Strichartz estimates for an inhomogeneous Maxwell system","authors":"P. D’Ancona, R. Schnaubelt","doi":"10.1080/03605302.2021.1998910","DOIUrl":"https://doi.org/10.1080/03605302.2021.1998910","url":null,"abstract":"Abstract We show global-in-time Strichartz estimates for the isotropic Maxwell system with divergence free data. On the scalar permittivity and permeability we impose decay assumptions as and a non-trapping condition. The proof is based on smoothing estimates in weighted L 2 spaces which follow from corresponding resolvent estimates for the underlying Helmholtz problem.","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47184900","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}
引用次数: 4
Inhomogeneous global minimizers to the one-phase free boundary problem 无相边界问题的非齐次全局极小化
IF 1.9 2区 数学
Communications in Partial Differential Equations Pub Date : 2021-06-28 DOI: 10.1080/03605302.2022.2051187
D. De Silva, D. Jerison, H. Shahgholian
{"title":"Inhomogeneous global minimizers to the one-phase free boundary problem","authors":"D. De Silva, D. Jerison, H. Shahgholian","doi":"10.1080/03605302.2022.2051187","DOIUrl":"https://doi.org/10.1080/03605302.2022.2051187","url":null,"abstract":"Abstract Given a global 1-homogeneous minimizer U 0 to the Alt-Caffarelli energy functional, with we provide a foliation of the half-space with dilations of graphs of global minimizers with analytic free boundaries at distance 1 from the origin.","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2021-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41960971","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}
引用次数: 6
Small data global regularity for half-wave maps in n = 4 dimensions. n = 4维半波图的小数据全局正则性。
IF 1.9 2区 数学
Communications in Partial Differential Equations Pub Date : 2021-06-15 eCollection Date: 2021-01-01 DOI: 10.1080/03605302.2021.1936021
Anna Kiesenhofer, Joachim Krieger
{"title":"Small data global regularity for half-wave maps in <i>n</i> = 4 dimensions.","authors":"Anna Kiesenhofer,&nbsp;Joachim Krieger","doi":"10.1080/03605302.2021.1936021","DOIUrl":"https://doi.org/10.1080/03605302.2021.1936021","url":null,"abstract":"<p><p>We prove that the half-wave maps problem on <math> <mrow> <msup><mrow><mi>R</mi></mrow> <mrow><mn>4</mn> <mo>+</mo> <mn>1</mn></mrow> </msup> </mrow> </math> with target <i>S</i> <sup>2</sup> is globally well-posed for smooth initial data which are small in the critical <i>l</i> <sup>1</sup> based Besov space. This is a formal analogue of the result proved by Tataru for wave maps.</p>","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2021-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/03605302.2021.1936021","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39578400","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}
引用次数: 5
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