Scattering profile for global solutions of the energy-critical wave equation

被引：14

作者：

Duyckaerts, Thomas ^{[1
]}

Kenig, Carlos ^{[2
]}

Merle, Frank ^{[3
]}

机构：

[1] Univ Paris 13, LAGA, Sorbonne Paris Cite, UMR 7539, 99 Ave Jean Baptiste Clement, F-93430 Villetaneuse, France

[2] Univ Chicago, 5734 Univ Ave, Chicago, IL 60637 USA

[3] IHES, Cergy Pontoise UMR 8088, 2 Av Adolphe Chauvin, F-95302 Cergy Pontoise, France

来源：

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY | 2019年 / 21卷 / 07期

基金：

欧洲研究理事会;

关键词：

Wave equation; critical nonlinearity; global solution; radiation term; STRICHARTZ INEQUALITIES; RADIAL SOLUTIONS; BLOW-UP; REGULARITY; ATTRACTOR;

D O I：

10.4171/JEMS/882

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Consider the focusing energy-critical wave equation in space dimension 3, 4 or 5. We prove that any global solution which is bounded in the energy space converges in the exterior of wave cones to a radiation term which is a solution of the linear wave equation.

引用

页码：2117 / 2162

页数：46

共 50 条

[31] Dynamics of radial threshold solutions for generalized energy-critical Hartree equation
Li, Xuemei
Liu, Chenxi
Tang, Xingdong
Xu, Guixiang
FORUM MATHEMATICUM, 2025,
[32] Soliton Resolution for the Energy-Critical Nonlinear Wave Equation in the Radial Case
Jacek Jendrej
Andrew Lawrie
Annals of PDE, 2023, 9
[33] Construction of type II blow-up solutions for the energy-critical wave equation in dimension 5
Jendrej, Jacek
JOURNAL OF FUNCTIONAL ANALYSIS, 2017, 272 (03) : 866 - 917
[34] The energy-critical nonlinear wave equation with an inverse-square potential
Miao, Changxing
Murphy, Jason
Zheng, Jiqiang
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2020, 37 (02): : 417 - 456
[35] The Focusing Energy-Critical Nonlinear Wave Equation With Random Initial Data
Kenig, Carlos
Mendelson, Dana
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2021, 2021 (19) : 14508 - 14615
[36] Universality of the blow-up profile for small type II blow-up solutions of the energy-critical wave equation: the nonradial case
Duyckaerts, Thomas
Kenig, Carlos
Merle, Frank
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2012, 14 (05) : 1389 - 1454
[37] On multi-solitons for the energy-critical wave equation in dimension 5
Yuan, Xu
NONLINEARITY, 2019, 32 (12) : 5017 - 5048
[38] CONSTRUCTION OF TWO-BUBBLE SOLUTIONS FOR ENERGY-CRITICAL WAVE EQUATIONS
Jendrej, Jacek
AMERICAN JOURNAL OF MATHEMATICS, 2019, 141 (01) : 55 - 118
[39] The focusing energy-critical Hartree equation
Li, Dong
Miao, Changxing
Zhang, Xiaoyi
JOURNAL OF DIFFERENTIAL EQUATIONS, 2009, 246 (03) : 1139 - 1163
[40] ALMOST SURE SCATTERING FOR THE 4D ENERGY-CRITICAL DEFOCUSING NONLINEAR WAVE EQUATION WITH RADIAL DATA
Dodson, Benjamin
Luehrmann, Jonas
Mendelson, Dana
AMERICAN JOURNAL OF MATHEMATICS, 2020, 142 (02) : 475 - 504

← 1 2 3 4 5 →