Global existence of solutions for a fourth-order nonlinear Schrodinger equation in n+1 dimensions

被引：11

作者：

Guo, Cuihua ^{[1
]}

机构：

[1] Shanxi Univ, Sch Math Sci, Taiyuan 030006, Shanxi, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2010年 / 73卷 / 02期

基金：

美国国家科学基金会;

关键词：

Fourth-order Schrodinger equation; Cauchy problem; Global existence; I-method; WELL-POSEDNESS; SOLITONS;

D O I：

10.1016/j.na.2010.03.052

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the global well-posedness for the Cauchy problem of the fourth-order nonlinear Schrodinger equation iu(t) + lambda Delta u + mu Delta(2)u + v vertical bar u vertical bar(2m)u = 0, x is an element of R-n, t is an element of R. By using the I-method, we prove that if s > 1 + mn-9 + root(4m-mn+7)(2) + 16/4m, then the Cauchy problem is globally well-posed in H-s(R-n) for either the case lambda < 0, mu > 0, v > 0 or the case lambda > 0, mu < 0, v < 0 with m, n satisfying some conditions. (C) 2010 Elsevier Ltd. All rights reserved.

引用

页码：555 / 563

页数：9

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