Universality of blow-up profile for small radial type II blow-up solutions of the energy-critical wave equation

被引:113
作者
Duyckaerts, Thomas [1 ]
Kenig, Carlos [2 ]
Merle, Frank [1 ]
机构
[1] Univ Cergy Pontoise, Dept Math, F-95302 Cergy Pontoise, France
[2] Univ Chicago, Dept Math, Chicago, IL 60637 USA
基金
美国国家科学基金会;
关键词
NONLINEAR SCHRODINGER-EQUATION; (1+2)-DIMENSIONAL MINKOWSKI SPACE; GLOBAL WELL-POSEDNESS; MAPS; SCATTERING; STABILITY; EXISTENCE;
D O I
10.4171/JEMS/261
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Consider the energy-critical focusing wave equation on the Euclidian space. A blow-up type II solution of this equation is a solution which has finite time of existence but stays bounded in the energy space. The aim of this work is to exhibit universal properties of such solutions. Let W be the unique radial positive stationary solution of the equation. Our main result is that in dimension 3, under an appropriate smallness assumption, any type II blow-up radial solution is essentially the sum of a rescaled W concentrating at the origin and a small remainder which is continuous with respect to the time variable in the energy space. This is coherent with the solutions constructed by Krieger, Schlag and Tataru. One ingredient of our proof is that the unique radial solution which is compact up to scaling is equal to W up to symmetries.
引用
收藏
页码:533 / 599
页数:67
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