Global well-posedness, scattering and blow-up for the energy-critical focusing non-linear wave equation

被引：308
|
作者：
Kenig, Carlos E. [1 ]
Merle, Frank [2 ]
机构：
[1] Univ Chicago, Dept Math, Chicago, IL 60637 USA
[2] Univ Cergy Pontoise, Dept Math, FR-95302 Cergy Pontoise, France
来源：
ACTA MATHEMATICA | 2008年 / 201卷 / 02期
关键词：
D O I：
10.1007/s11511-008-0031-6
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study the energy-critical focusing non-linear wave equation, with data in the energy space, in dimensions 3, 4 and 5. We prove that for Cauchy data of energy smaller than the one of the static solution W which gives the best constant in the Sobolev embedding, the following alternative holds. If the initial data has smaller norm in the homogeneous Sobolev space H 1 than the one of W, then we have global well-posedness and scattering. If the norm is larger than the one of W, then we have break-down in finite time.
引用
收藏
页码：147 / 212
页数：66
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