January  2007, 17(1): 181-200. doi: 10.3934/dcds.2007.17.181

Global well-posedness of the Cauchy problem for nonlinear Schrödinger-type equations

1. 

Institute of Applied Physics and Computational Mathematics, PO Box 8009, Beijing 100088, China

2. 

Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing 100080, China

Received  September 2004 Revised  August 2006 Published  October 2006

In this paper the global well-posedness in $L^2$ and $H^m$ of the Cauchy problem is proved for nonlinear Schrödinger-type equations. This we do by establishing regular Strichartz estimates for the corresponding linear equations and some nonlinear a priori estimates in the framework of Besov spaces. We further establish the regularity of the $H^m$-solution to the Cauchy problem.
Citation: Changxing Miao, Bo Zhang. Global well-posedness of the Cauchy problem for nonlinear Schrödinger-type equations. Discrete and Continuous Dynamical Systems, 2007, 17 (1) : 181-200. doi: 10.3934/dcds.2007.17.181
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