| | 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
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