Global existence for semilinear Schrodinger equations in 2+1 dimensions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:337

Article

Wang, Hua¹  Cui, Shangbin¹ 

[1] Sun Yat Sen Univ, Inst Math, Guangzhou 510275, Guangdong, Peoples R China

关键词: semilinear Schrodinger equation;    initial value problem;    global existence;    1-method;   

DOI  :  10.1016/j.jmaa.2007.03.099

来源: Elsevier

【 摘 要 】

This paper is concerned with global well-posedness of the 2-dimensional defocusing semilinear Schrodinger equation iu(t) + Delta u = vertical bar u vertical bar(2m) u in the Sobolev space H-s(R-2). In a previous work of Guo and Cui [C. Guo, S. Cui, Global existence for 2D nonlinear Schrodinger equations via high-low frequency decomposition method, J. Math. Anal. Appl. 324 (2006) 882-907] it was proved that global well-posedness holds in H-s(R-2) for s > 10m-6/10m-5. That result is obtained by using the high-low frequency decomposition method. In this paper we apply the 1-method to improve that result, and prove that global well-posedness holds in H-s(R-2) for s > 1 - 5-root 17/4m. (C) 2007 Elsevier Inc. All rights reserved.

【 授权许可】

Free