Mathematical aspects of nonlinear dispersive equations / Jean Bourgain, Carlos E. Kenig, and S. Klainerman, editors.

Format:

Book

Contributor:

Bourgain, Jean, 1954-2018.

Kenig, Carlos E., 1953-

Klainerman, Sergiu, 1950-

Series:

Annals of mathematics studies ; no. 163.

Annals of mathematics studies ; no. 163

Language:

English

Subjects (All):

Differential equations, Nonlinear--Congresses.

Differential equations, Nonlinear.

Nonlinear partial differential operators--Congresses.

Nonlinear partial differential operators.

Genre:

Conference papers and proceedings.

Physical Description:

vi, 300 pages : illustrations ; 24 cm.

Place of Publication:

Princeton : Princeton University Press, 2007.

Summary:

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, Schrö dinger operators, nonlinear Schrö dinger and wave equations, and the Euler and Navier-Stokes equations.

Contents:

Chapter 1 On Strichartz's Inequalities and the Nonlinear Schrodinger Equation on Irrational Tori / J. Bourgain 1

Chapter 2 Diffusion Bound for a Nonlinear Schrodinger Equation / J. Bourgain, W.-M. Wang 21

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

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

Chapter 5 Global Solutions for the Nonlinear Schrodinger Equation on Three-Dimensional Compact Manifolds / N. Burq, P. Gerard, N. Tzvetkov 111

Chapter 6 Power Series Solution of a Nonlinear Schrodinger 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, J. Szeftel 171

Chapter 9 Local and Global Wellposedness of Periodic KP-I Equations / A. D. Ionescu, C. E. Kenig 181

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

Chapter 11 Longtime Decay Estimates for the Schrodinger Equation on Manifolds / I. Rodnianski, T. Tao 223

Chapter 12 Dispersive Estimates for Schrodinger Operators: A Survey / W. Schlag 255.

Notes:

"This book contains the written accounts of a number of lectures given during the CMI/IAS Workshop on mathematical aspects of nonlinear PDEs in the spring of 2004 at the Institute for Advanced Study in Princeton, New Jersey."--Preface.

Includes bibliographical references and index.

ISBN:

069112860X

9780691128603

069112955X

9780691129556

OCLC:

71045168

Online:

Contributor biographical information

Publisher description