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

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Mathematical Aspects of Nonlinear Dispersive Equations (Am-163) (Annals of Mathematics Studies) Cover

 

Synopses & Reviews

Publisher Comments:

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.

Table of Contents

Preface vii

Chapter 1. On Strichartz's Inequalities and the Nonlinear Schrödinger

Equation on Irrational Tori by J. Bourgain 1

Chapter 2. Diffusion Bound for a Nonlinear Schrödinger Equation by J. Bourgain and W.-M.Wang 21

Chapter 3. Instability of Finite Difference Schemes for Hyperbolic Conservation Laws by A. Bressan, P. Baiti, and H. K. Jenssen 43

Chapter 4. Nonlinear Elliptic Equations with Measures Revisited H. Brezis, M. Marcus, and A. C. Ponce 55

Chapter 5. Global Solutions for the Nonlinear Schrödinger Equation on Three-Dimensional Compact Manifolds by N. Burq, P. Gérard, and N. Tzvetkov 111

Chapter 6. Power Series Solution of a Nonlinear Schrödinger Equation by M. Christ 131

Chapter 7. Eulerian-Lagrangian Formalism and Vortex Reconnection by P. Constantin 157

Chapter 8. Long Time Existence for Small Data Semilinear Klein-Gordon Equations on Spheres by J.-M. Delort and J. Szeftel 171

Chapter 9. Local and GlobalWellposedness of Periodic KP-I Equations by A. D. Ionescu and C. E. Kenig 181

Chapter 10. The Cauchy Problem for the Navier-Stokes Equations with Spatially Almost Periodic Initial Data by Y. Giga, A. Mahalov, and B. Nicolaenko 213

Chapter 11. Longtime Decay Estimates for the Schrödinger Equation

on Manifolds by I. Rodnianski and T. Tao 223

Chapter 12. Dispersive Estimates for Schrödinger Operators: A Survey by W. Schlag 255

Contributors 287

Index 291

Product Details

ISBN:
9780691128603
Author:
Bourgain, Jean
Publisher:
Princeton University Press
Editor:
Kenig, Carlos E.
Editor:
Klainerman, S.
Editor:
Klainerman, Sergiu
Author:
Kenig, Carlos E.
Author:
Klainerman, Sergiu
Location:
Princeton
Subject:
Differential Equations
Subject:
Differential equations, nonlinear
Subject:
Nonlinear partial differential operators.
Subject:
Mathematics
Subject:
Mathematics-Differential Equations
Copyright:
Edition Description:
Hardcover
Series:
Annals of Mathematics Studies
Series Volume:
163
Publication Date:
April 2007
Binding:
Hardback
Grade Level:
College/higher education:
Language:
English
Illustrations:
Y
Pages:
296
Dimensions:
9 x 6 in

Related Subjects

Science and Mathematics » Mathematics » Differential Equations

Mathematical Aspects of Nonlinear Dispersive Equations (Am-163) (Annals of Mathematics Studies) Used Hardcover
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