GLOBAL WELL-POSEDNESS AND SCATTERING FOR THE DEFOCUSING, CUBIC NONLINEAR SCHRODINGER EQUATION WHEN n=3 VIA A LINEAR-NONLINEAR DECOMPOSITION

被引：9
作者：
Dodson, Benjamin [1 ]
机构：
[1] UC Berkeley Math, Berkeley, CA 94720 USA
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2013年 / 33卷 / 05期
基金：
美国国家科学基金会;
关键词：
Nonlinear Schrodinger equation; ROUGH SOLUTIONS; CAUCHY-PROBLEM; DECAY; NLS;
D O I：
10.3934/dcds.2013.33.1905
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we prove global well-posedness and scattering for the defocusing, cubic nonlinear Schrodinger equation when n = 3 and u(0) 2 H-s (R-3), s > 5/7. To this end, we utilize a linear-nonlinear decomposition, similar to the decomposition used in [20] for the wave equation.
引用
收藏
页码：1905 / 1926
页数：22
相关论文
共 29 条
  • [1] [Anonymous], 1993, Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals
  • [2] Scattering in the energy space and below for 3D NLS
    Bourgain, J
    [J]. JOURNAL D ANALYSE MATHEMATIQUE, 1998, 75 (1): : 267 - 297
  • [3] Bourgain J, 1998, INT MATH RES NOTICES, V1998, P253
  • [4] Bourgain J, 1999, AM MATH SOC C PUBLIC
  • [5] THE CAUCHY-PROBLEM FOR THE CRITICAL NONLINEAR SCHRODINGER-EQUATION IN HS
    CAZENAVE, T
    WEISSLER, FB
    [J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1990, 14 (10) : 807 - 836
  • [6] THE CAUCHY-PROBLEM FOR THE NONLINEAR SCHRODINGER-EQUATION IN H-1
    CAZENAVE, T
    WEISSLER, FB
    [J]. MANUSCRIPTA MATHEMATICA, 1988, 61 (04) : 477 - 494
  • [7] Cazenave T., 1996, An Introduction to Nonlinear Schrodinger Equations
  • [8] Colliander J, 2008, DISCRETE CONT DYN-A, V21, P665
  • [9] Global existence and scattering for rough solutions of a nonlinear Schrodinger equation on R3
    Colliander, J
    Keel, M
    Staffilani, G
    Takaoka, H
    Tao, T
    [J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2004, 57 (08) : 987 - 1014
  • [10] Colliander J, 2002, MATH RES LETT, V9, P659
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