# American Institute of Mathematical Sciences

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 & Continuous Dynamical Systems, 2007, 17 (1) : 181-200. doi: 10.3934/dcds.2007.17.181
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