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

Changxing Miao; Bo Zhang

doi:10.3934/dcds.2007.17.181

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2007, Volume 17, Issue 1: 181-200. Doi: 10.3934/dcds.2007.17.181

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

Changxing Miao^1, and
Bo Zhang^2,

1.
Institute of Applied Physics and Computational Mathematics, PO Box 8009, Beijing 100088
2.
Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing 100080

Received: September 2004

Revised: August 2006

Published: January 2007

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Abstract

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.

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Mathematics Subject Classification: Primary: 35Q55, 37L05.

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