Critical non-linear dispersive equations: global existence, scattering, blow-up and universal profiles

被引：1
|
作者：
Kenig, Carlos [1 ]
机构：
[1] Univ Chicago, Dept Math, Chicago, IL 60637 USA
来源：
JAPANESE JOURNAL OF MATHEMATICS | 2011年 / 6卷 / 02期
关键词：
critical non-linear dispersive equation; global existence; scattering; finite time blow-up; universal profiles; SCHRODINGER-EQUATION; WAVE MAPS; WELL-POSEDNESS; CAUCHY-PROBLEM; ASYMPTOTIC-BEHAVIOR; RADIAL DATA; ENERGY; REGULARITY; SPACE; TIME;
D O I：
10.1007/s11537-011-1108-0
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We discuss recent progress in the understanding of the global behavior of solutions to critical non-linear dispersive equations. The emphasis is on global existence, scattering and finite time blow-up. For solutions that are bounded in the critical norm, but which blow-up in finite time, we also discuss the issue of universal profiles at the blow-up time.
引用
收藏
页码：121 / 141
页数：21
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