log-log blow up solutions blow up at exactly m points

被引:9
作者
Fan, Chenjie [1 ]
机构
[1] MIT, Dept Math, 77 Massachusetts Ave, Cambridge, MA 02139 USA
来源
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 2017年 / 34卷 / 06期
基金
美国国家科学基金会;
关键词
NLS; log-log blow up; m points blow up; Bootstrap; Propagation of regularity; Topological argument; NONLINEAR SCHRODINGER-EQUATION; STABILITY; NLS; CONSTRUCTION; EXISTENCE; SPHERE; MASS;
D O I
10.1016/j.anihpc.2016.11.002
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We study the focusing mass-critical nonlinear Schrodinger equation, and construct certain solutions which blow up at exactly m points according to the log-log law. (C) 2016 Elsevier Masson SAS. All rights reserved.
引用
收藏
页码:1429 / 1482
页数:54
相关论文
共 30 条
[11]   RATE OF BLOWUP FOR SOLUTIONS OF THE NONLINEAR SCHRODINGER-EQUATION AT CRITICAL DIMENSION [J].
LANDMAN, MJ ;
PAPANICOLAOU, GC ;
SULEM, C ;
SULEM, PL .
PHYSICAL REVIEW A, 1988, 38 (08) :3837-3843
[12]  
Martel Y., 2015, ARXIV151200900
[13]   DETERMINATION OF BLOW-UP SOLUTIONS WITH MINIMAL MASS FOR NONLINEAR SCHRODINGER-EQUATIONS WITH CRITICAL POWER [J].
MERLE, F .
DUKE MATHEMATICAL JOURNAL, 1993, 69 (02) :427-454
[14]   On a sharp lower bound on the blow-up rate for the L2 critical nonlinear Schrodinger equation [J].
Merle, F ;
Raphael, P .
JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2006, 19 (01) :37-90
[15]   On one blow up point solutions to the critical nonlinear Schrodinger equation [J].
Merle, F .
JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS, 2005, 2 (04) :919-962
[16]   The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schrodinger equation [J].
Merle, F ;
Raphael, P .
ANNALS OF MATHEMATICS, 2005, 161 (01) :157-222
[17]   Profiles and quantization of the blow up mass for critical nonlinear Schrodinger equation [J].
Merle, F ;
Raphael, P .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2005, 253 (03) :675-704
[18]   On universality of blow-up profile for L2 critical nonlinear Schrodinger equation [J].
Merle, F ;
Raphael, P .
INVENTIONES MATHEMATICAE, 2004, 156 (03) :565-672
[19]   Sharp upper bound on the blow-up rate for the critical nonlinear Schrodinger equation [J].
Merle, F ;
Raphael, P .
GEOMETRIC AND FUNCTIONAL ANALYSIS, 2003, 13 (03) :591-642
[20]   SOLUTION OF A NONLINEAR HEAT-EQUATION WITH ARBITRARILY GIVEN BLOW-UP POINTS [J].
MERLE, F .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1992, 45 (03) :263-300