Mathematical Aspects of Nonlinear Dispersive Equations (AM-163) (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. Contents Preface Chapter 1. On Strichartz’s Inequalities and the Nonlinear Schrödinger Equation on Irrational Tori Chapter 2. Diffusion Bound for a Nonlinear Schrödinger Equation Chapter 3. Instability of Finite Difference Schemes for Hyperbolic Conservation Laws Chapter 4. Nonlinear Elliptic Equations with Measures Revisited Chapter 5. Global Solutions for the Nonlinear Schrödinger Equation on Three-Dimensional Compact Manifolds Chapter 6. Power Series Solution of a Nonlinear Schrödinger Equation Chapter 7. Eulerian-Lagrangian Formalism and Vortex Reconnection Chapter 8. Long Time Existence for Small Data Semilinear Klein-Gordon Equations on Spheres Chapter 9. Local and Global Wellposedness of Periodic KP-I Equations Chapter 10. The Cauchy Problem for the Navier-Stokes Equations with Spatially Almost Periodic Initial Data Chapter 11. Longtime Decay Estimates for the Schrödinger Equation on Manifolds Contributors Index 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, Schrodinger operators