Mathematical Aspects of Nonlinear Dispersive Equations

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).

• Preface vii Chapter 1. On Strichartz's Inequalities and the Nonlinear Schrodinger Equation on Irrational Tori by J. Bourgain 1 Chapter 2. Diffusion Bound for a Nonlinear Schrodinger 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 Schrodinger Equation on Three-Dimensional Compact Manifolds by N. Burq, P. Gerard, and N. Tzvetkov 111 Chapter 6. Power Series Solution of a Nonlinear Schrodinger 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 Schrodinger Equation on Manifolds by I. Rodnianski and T. Tao 223 Chapter 12. Dispersive Estimates for Schrodinger Operators: A Survey by W. Schlag 255 Contributors 287 Index 291

"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