GLOBAL WELL-POSEDNESS OF CRITICAL NONLINEAR SCHRODINGER EQUATIONS BELOW L2

被引：13
作者：
Cho, Yonggeun [1 ,2 ]
Hwang, Gyeongha [3 ]
Ozawa, Tohru [4 ]
机构：
[1] Chonnam Natl Univ, Dept Math, Jeonju 561756, South Korea
[2] Chonnam Natl Univ, Inst Pure & Appl Math, Jeonju 561756, South Korea
[3] Seoul Natl Univ, Dept Math Sci, Seoul 151747, South Korea
[4] Waseda Univ, Dept Appl Phys, Tokyo 1698555, Japan
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2013年 / 33卷 / 04期
基金：
新加坡国家研究基金会;
关键词：
Hartree equations; global well-posedness; critical nonlinearity below L-2; weighted Strichartz estimate; angular regularity; DEFOCUSING HARTREE EQUATION; SCATTERING; SPACE; WAVES;
D O I：
10.3934/dcds.2013.33.1389
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The global well-posedness on the Cauchy problem of nonlinear Schrodinger equations (NLS) is studied for a class of critical nonlinearity below L-2 in small data setting. We consider Hartree type (HNLS) and inhomogeneous power type NLS (PNLS). Since the critical Sobolev index s(c) is negative, it is rather difficult to analyze the nonlinear term. To overcome the difficulty we combine weighted Strichartz estimates in polar coordinates with new Duhamel estimates involving angular regularity.
引用
收藏
页码：1389 / 1405
页数：17
相关论文
共 37 条
[1]   Lorentz space extension of Strichartz estimates [J].
Ahn, C ;
Cho, Y .
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2005, 133 (12) :3497-3503
[2]   Soliton stability versus collapse [J].
Bergé, L .
PHYSICAL REVIEW E, 2000, 62 (03) :R3071-R3074
[3]  
Bouard A., 2005, ANN IHP, V6, P1
[4]  
Carothers N. L., 2005, LONDON MATH SOC STUD
[5]  
Cazenave T, 2003, Semilinear Schrodinger Equations
[6]   Mixed Norm Estimates of Schrodinger Waves and Their Applications [J].
Chae, Myeongju ;
Cho, Yonggeun ;
Lee, Sanghyuk .
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2010, 35 (05) :906-943
[7]  
Cho Y., 2009, DISCRETE CONTIN DYN, V23, P1273
[8]  
Cho Y., INDIANA U M IN PRESS
[9]  
Cho Y., 2010, RIMS KOKYUROKU BES B, VB22, P145
[10]   On Hartree equations with derivatives [J].
Cho, Yonggeun ;
Lee, Sanghyuk ;
Ozawa, Tohru .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (06) :2094-2108
1234