Mathematical Aspects of Nonlinear Dispersive Equations (AM-163)

by Jean Bourgain, Carlos E. Kenig, Sergiu Klainerman

Overview

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.

Product Details

ISBN-13:	9780691129556
Publisher:	Princeton University Press
Publication date:	04/29/2007
Series:	Annals of Mathematics Studies , #163
Pages:	296
Product dimensions:	6.00(w) x 9.25(h) x (d)
Age Range:	18 Years

About the Author

Jean Bourgain is Professor of Mathematics at the Institute for Advanced Study in Princeton. In 1994, he won the Fields Medal. He is the author of Green's Function Estimates for Lattice Schrödinger Operators and Applications (Princeton). Carlos E. Kenig is Professor of Mathematics at the University of Chicago. He is a fellow of the American Academy of Arts and Sciences and the author of Harmonic Analysis Techniques for Second Order Elliptic Boundary Value Problems. S. Klainerman is Professor of Mathematics at Princeton University. He is a MacArthur Fellow and Bocher Prize recipient. He is the coauthor of The Global Nonlinear Stability of the Minkowski Space (Princeton).

Table of Contents

Contents

Preface....................vii
Chapter 1. On Strichartz's Inequalities and the Nonlinear Schrödinger Equation on Irrational Tori J. Bourgain....................1
Chapter 2. Diffusion Bound for a Nonlinear Schrödinger Equation J. Bourgain and W.-M.Wang....................21
Chapter 3. Instability of Finite Difference Schemes for Hyperbolic Conservation Laws 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 N. Burq, P. Gérard, and N. Tzvetkov....................111
Chapter 6. Power Series Solution of a Nonlinear Schrödinger Equation M. Christ....................131
Chapter 7. Eulerian-Lagrangian Formalism and Vortex Reconnection P. Constantin....................157
Chapter 8. Long Time Existence for Small Data Semilinear Klein-Gordon Equations on Spheres J.-M. Delort and J. Szeftel....................171
Chapter 9. Local and Global Wellposedness of Periodic KP-I Equations A. D. Ionescu and C. E. Kenig....................181
Chapter 10. The Cauchy Problem for the Navier-Stokes Equations with Spatially Almost Periodic Initial Data Y. Giga, A. Mahalov, and B. Nicolaenko....................213
Chapter 11. Longtime Decay Estimates for the Schrödinger Equation on Manifolds I. Rodnianski and T. Tao....................223
Chapter 12. Dispersive Estimates for Schrödinger Operators: A Survey W. Schlag....................255
Contributors....................287
Index....................291

Editorial Reviews

"The volume contains valuable contributions to the area of nonlinear PDEs, making it indispensable for all researchers interested in partial differential equations and their applications."—-Radu Precup, Mathematica

From the Publisher

The volume contains valuable contributions to the area of nonlinear PDEs, making it indispensable for all researchers interested in partial differential equations and their applications.

Mathematica - Radu Precup

The volume contains valuable contributions to the area of nonlinear PDEs, making it indispensable for all researchers interested in partial differential equations and their applications.
— Radu Precup

Mathematica