STABLE SELF-SIMILAR BLOW-UP DYNAMICS FOR SLIGHTLY L2 SUPER-CRITICAL NLS EQUATIONS

被引：33

作者：

Merle, Frank ^{[1
,2
]}

Raphael, Pierre ^{[3
]}

Szeftel, Jeremie ^{[4
,5
]}

机构：

[1] Univ Cergy Pontoise, Dept LAGA, F-95302 Cergy Pontoise, France

[2] Inst Hautes Etud Sci, F-91440 Bures Sur Yvette, France

[3] Inst Math Toulouse, F-31062 Toulouse 9, France

[4] Ecole Normale Super, Dept Math & Applicat, CNRS, F-75230 Paris 05, France

[5] Princeton Univ, Dept Math, Princeton, NJ 08544 USA

来源：

GEOMETRIC AND FUNCTIONAL ANALYSIS | 2010年 / 20卷 / 04期

关键词：

Nonlinear Schrodinger equation; blow up; supercritical; NONLINEAR SCHRODINGER-EQUATION; STABILITY; SINGULARITY; WAVES;

D O I：

10.1007/s00039-010-0081-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the focusing nonlinear Schrodinger equations i partial derivative(t)u+ Delta u + u vertical bar u vertical bar (p- 1) = 0 in dimension 1 <= N <= 5 and for slightly L-2 super- critical nonlinearities p(c) < p < (1 + epsilon) p(c) with p(c) = 1+ 4/N and 0 < epsilon << 1. We prove the existence and stability in the energy space H-1 of a self- similar finite- time blow- up dynamics and provide a qualitative description of the singularity formation near the blow-up time.

引用

页码：1028 / 1071

页数：44

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