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

[21] ALMOST-SURE SCATTERING FOR THE RADIAL ENERGY-CRITICAL NONLINEAR WAVE EQUATION IN THREE DIMENSIONS
Bringmann, Bjoern
ANALYSIS & PDE, 2020, 13 (04): : 1011 - 1050
[22] Global well-posedness, scattering and blow-up for the energy-critical focusing non-linear wave equation
Kenig, Carlos E.
Merle, Frank
ACTA MATHEMATICA, 2008, 201 (02) : 147 - 212
[23] SPACETIME INTEGRAL BOUNDS FOR THE ENERGY-CRITICAL NONLINEAR WAVE EQUATION
Dodson, Benjamin
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2024, 152 (03) : 1169 - 1180
[24] Global well-posedness and scattering for the energy-critical, defocusing Hartree equation for radial data
Miao, Changxing
Xu, Guixiang
Zhao, Lifeng
JOURNAL OF FUNCTIONAL ANALYSIS, 2007, 253 (02) : 605 - 627
[25] Global infinite energy solutions of the critical semilinear wave equation
Germain, Pierre
REVISTA MATEMATICA IBEROAMERICANA, 2008, 24 (02) : 463 - 497
[26] Universality of blow-up profile for small radial type II blow-up solutions of the energy-critical wave equation
Duyckaerts, Thomas
Kenig, Carlos
Merle, Frank
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2011, 13 (03) : 533 - 599
[27] Global Well-Posedness and Scattering for the Energy-Critical, Defocusing Hartree Equation in 1+n
Miao, Changxing
Xu, Guixiang
Zhao, Lifeng
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2011, 36 (05) : 729 - 776
[28] Global well-posedness and scattering for the energy-critical nonlinear Schrodinger equation in R3
Colliander, J.
Keel, M.
Staffilani, G.
Takaoka, H.
Tao, T.
ANNALS OF MATHEMATICS, 2008, 167 (03) : 767 - 865
[29] PROFILES FOR THE RADIAL FOCUSING ENERGY-CRITICAL WAVE EQUATION IN ODD DIMENSIONS
Rodriguez, Casey
ADVANCES IN DIFFERENTIAL EQUATIONS, 2016, 21 (5-6) : 505 - 570
[30] Soliton Resolution for the Energy-Critical Nonlinear Wave Equation in the Radial Case
Jendrej, Jacek
Lawrie, Andrew
ANNALS OF PDE, 2023, 9 (02)

← 1 2 3 4 5 →