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Global Solutions of Nonlinear Schrödinger Equations
J. Bourgain, Institute for Advanced Study, Princeton, NJ
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Colloquium Publications
1999; 182 pp; hardcover
Volume: 46
ISBN-10: 0-8218-1919-4
ISBN-13: 978-0-8218-1919-7
List Price: US$41
Member Price: US$32.80
Order Code: COLL/46
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This volume presents recent progress in the theory of nonlinear dispersive equations, primarily the nonlinear Schrödinger (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.

Readership

Graduate students and research mathematicians interested in PDEs and related areas.

Table of Contents

  • Introduction and summary
  • An overview of results on the Cauchy problem for NLS
  • Further comments
  • 3D \(H^1\)-critical defocusing NLS
  • Global wellposedness below energy norm
  • Nonlinear Schrödinger equation with periodic boundary conditions
  • Growth of Sobolev norms in linear Schrödinger equations with smooth time dependent potential
  • Zakharov systems
  • References
  • Index
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