GLOBAL EXISTENCE FOR THE CUBIC NONLINEAR SCHRODINGER EQUATION IN LOWER ORDER SOBOLEV SPACES

被引：0

作者：

Hayashi, Nakao ^{[1
]}

Naumkin, Pavel I. ^{[2
]}

机构：

[1] Osaka Univ, Dept Math, Grad Sch Sci, Toyonaka, Osaka 5600043, Japan

[2] Inst Matemat, Morelia 58089, Michoacan, Mexico

来源：

DIFFERENTIAL AND INTEGRAL EQUATIONS | 2011年 / 24卷 / 9-10期

关键词：

SCATTERING;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the Cauchy problem for the cubic nonlinear Schrodinger equation {iu(t) + 1/2u(xx) = u(3), x is an element of R, t > 0, u(0, x) = u(0)(x), x is an element of R. (0.1) The aim of the present paper is to consider problem (0.1) in low-order Sobolev spaces, when the initial data u(0) is an element of H(alpha) boolean AND H(0,alpha) with alpha >1/2. In our previous paper [7] we proved the global existence of solutions to (0.1) if the initial data u(0) is an element of H(2) boolean AND H(0,2). Also we find the large-time asymptotics of solutions.

引用

页码：801 / 828

页数：28

共 50 条

[21] SOLUTIONS FOR THE EQUATION OF NONLINEAR VIBRATIONS IN SOBOLEV SPACES OF FRACTIONARY ORDER
MEDEIROS, LA
MIRANDA, MM
[J]. MATEMATICA APLICADA E COMPUTACIONAL, 1987, 6 (03): : 257 - 276
[22] Global existence of solutions for the Kawahara equation in Sobolev spaces of negative indices
Wang, Hua
Cui, Shang Bin
Deng, Dong Gao
[J]. ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2007, 23 (08) : 1435 - 1446
[23] Global Existence of Solutions for the Kawahara Equation in Sobolev Spaces of Negative Indices
Hua Wang
Shang Bin Cui
Dong Gao Deng
[J]. Acta Mathematica Sinica, English Series, 2007, 23 : 1435 - 1446
[24] Notes on Global Existence for the Nonlinear Schrodinger Equation Involves Derivative
Zheng, Shi Yang
[J]. ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2014, 30 (10) : 1735 - 1747
[25] Global existence of small solutions to a relativistic nonlinear Schrodinger equation
deBouard, A
Hayashi, N
Saut, JC
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1997, 189 (01) : 73 - 105
[26] Global existence and scattering for the nonlinear Schrodinger equation on Schwarzschild manifolds
Laba, I
Soffer, A
[J]. HELVETICA PHYSICA ACTA, 1999, 72 (04): : 274 - 294
[27] Phenomena of Blowup and Global Existence of the Solution to a Nonlinear Schrodinger Equation
An, Xiaowei
Li, Desheng
Song, Xianfa
[J]. ABSTRACT AND APPLIED ANALYSIS, 2013,
[28] Global existence and compact attractors for the discrete nonlinear Schrodinger equation
Karachalios, NI
Yannacopoulos, AN
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2005, 217 (01) : 88 - 123
[29] Local and global existence in Lp for the inhomogeneous nonlinear Schrodinger equation
Wang, Deng
Yang, Han
[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2022, 45 (07) : 3497 - 3513
[30] Existence and uniqueness result for the Schrodinger-Poisson system and Hartree equation in Sobolev spaces
Ivanov, Angel
Venkov, George
[J]. JOURNAL OF EVOLUTION EQUATIONS, 2008, 8 (02) : 217 - 229

← 1 2 3 4 5 →