Mathematical Aspects of Nonlinear Dispersive Equations (AM-163) ：Mathematical Aspects of Nonlinear Dispersive Equations (AM-163) ( Annals of Mathematics Studies )

Publication subTitle ：Mathematical Aspects of Nonlinear Dispersive Equations (AM-163)

Publication series ：Annals of Mathematics Studies

Author： Bourgain Jean;Kenig Carlos E.;Klainerman Sergiu;  

Publisher： Princeton University Press‎

Publication year： 2009

E-ISBN: 9781400827794

P-ISBN(Paperback): 9780691128603

Subject： O1 Mathematics;O175 differential equations, integral equations

Keyword： 数学

Language： ENG

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Description

This collection of new and original papers on mathematical aspects of nonlinear dispersive equations includes both expository and technical papers that reflect a number of recent advances in the field. The expository papers describe the state of the art and research directions. The technical papers concentrate on a specific problem and the related analysis and are addressed to active researchers.

The book deals with many topics that have been the focus of intensive research and, in several cases, significant progress in recent years, including hyperbolic conservation laws, Schrödinger operators, nonlinear Schrödinger and wave equations, and the Euler and Navier-Stokes equations.

Chapter

Contents

Preface

Chapter 1. On Strichartz’s Inequalities and the Nonlinear Schrödinger Equation on Irrational Tori

Chapter 2. Diffusion Bound for a Nonlinear Schrödinger Equation

Chapter 3. Instability of Finite Difference Schemes for Hyperbolic Conservation Laws

Chapter 4. Nonlinear Elliptic Equations with Measures Revisited

Chapter 5. Global Solutions for the Nonlinear Schrödinger Equation on Three-Dimensional Compact Manifolds

Chapter 6. Power Series Solution of a Nonlinear Schrödinger Equation

Chapter 7. Eulerian-Lagrangian Formalism and Vortex Reconnection

Chapter 8. Long Time Existence for Small Data Semilinear Klein-Gordon Equations on Spheres

Chapter 9. Local and GlobalWellposedness of Periodic KP-I Equations

Chapter 10. The Cauchy Problem for the Navier-Stokes Equations with Spatially Almost Periodic Initial Data

Chapter 11. Longtime Decay Estimates for the Schrödinger Equation on Manifolds

Chapter 12. Dispersive Estimates for Schrödinger Operators: A Survey

Contributors

Index

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