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

页码：121 / 141

页数：21

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