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

被引：32
|
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.
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页码：1028 / 1071
页数：44
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