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Global solutions of nonlinear Schrödinger equations

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This volume presents recent progress in the theory of nonlinear dispersive equations, primarily the nonlinear Schrodinger (NLS) equation. The Cauchy problem for defocusing NLS with critical nonlinearity is discussed. New techniques and results are described on global existence and properties of solutions with large Cauchy data. Current research in harmonic analysis around Strichartz's inequalities and its relevance to nonlinear PDE is presented. Several topics in NLS theory on bounded domains are reviewed. Using the NLS as an example, the book offers comprehensive insight on current research related to dispersive equations and Hamiltonian PDEs.

Author(s): Jean Bourgain
Series: Colloquium Publications 46
Publisher: American Mathematical Society
Year: 1999

Language: English
Pages: viii+182
Tags: PDE; NLS equations

Cover
Title page
Contents
Introduction and summary
An overview of results on the Cauchy problem for NLS
Further comments
3D H¹-critical defocusing NLS
Global wellposedness below energy norm
Nonlinear Schrödinger equation with periodic boundary conditions
Appendix 1. Growth of Sobolev norms in linear Schrödinger equations with smooth time dependent potential
Appendix 2. Zakharov systems
References
Index
Back Cover