Mathematical Aspects of Nonlinear Dispersive Equations

Erscheinungsjahr 2007
ISBN: 978-0-691-12955-6
Verlag: Princeton University Press

Buch, Englisch, 296 Seiten, Format (B × H): 156 mm x 234 mm, Gewicht: 474 g

Reihe: Annals of Mathematics Studies

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.

Autoren/Hrsg.

Bourgain, Jean

Kenig, Carlos E.

Klainerman, Sergiu

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

Preface vii

Chapter 1. On Strichartz's Inequalities and the Nonlinear Schr?dinger

Equation on Irrational Tori by J. Bourgain 1

Chapter 2. Diffusion Bound for a Nonlinear Schr?dinger 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 Schr?dinger Equation on Three-Dimensional Compact Manifolds by N. Burq, P. G?rard, and N. Tzvetkov 111

Chapter 6. Power Series Solution of a Nonlinear Schr?dinger 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 Schr?dinger Equation

on Manifolds by I. Rodnianski and T. Tao 223

Chapter 12. Dispersive Estimates for Schr?dinger Operators: A Survey by W. Schlag 255

Contributors 287

Index 291

Über Autor(innen)

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 Schrodinger 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).