PROFILES FOR BOUNDED SOLUTIONS OF DISPERSIVE EQUATIONS, WITH APPLICATIONS TO ENERGY-CRITICAL WAVE AND SCHRODINGER EQUATIONS

被引：20
|
作者：
Duyckaerts, Thomas [1 ]
Kenig, Carlos E. [2 ]
Merle, Frank [3 ]
机构：
[1] Univ Paris 13, Inst Galilee, Sorbonne Paris Cite, LAGA UMR 7539, F-93430 Villetaneuse, France
[2] Univ Chicago, Dept Math, Chicago, IL 60637 USA
[3] AGM, Dept Math, F-95302 Cergy Pontoise, France
来源：
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2015年 / 14卷 / 04期
关键词：
Nonlinear dispersive equations; nonlinear wave and Schrodinger equations; bounded solutions; asymptotic behaviour; profile decomposition; GLOBAL WELL-POSEDNESS; BLOW-UP SOLUTIONS; RADIAL SOLUTIONS; SCATTERING; UNIVERSALITY; MAPS;
D O I：
10.3934/cpaa.2015.14.1275
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Consider a bounded solution of the focusing, energy-critical wave equation that does not scatter to a linear solution. We prove that this solution converges in some weak sense, along a sequence of times and up to scaling and space translation, to a sum of solitary waves. This result is a consequence of a new general compactness/rigidity argument based on profile decomposition. We also give an application of this method to the energy-critical Schrodinger equation.
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页码：1275 / 1326
页数：52
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