راه‌حل‌های جهانی معادلات غیرخطی شرودینگر

This volume presents recent progress in the theory of nonlinear dispersive equations, primarily the nonlinear Schrodinger (NLS) equation. The Cauchy problem for defocusing NLS with critical nonlinearity is discussed. New techniques and results are described on global existence and properties of solutions with large Cauchy data. Current research in harmonic analysis around Strichartz's inequalities and its relevance to nonlinear PDE is presented. Several topics in NLS theory on bounded domains are reviewed. Using the NLS as an example, the book offers comprehensive insight on current research related to dispersive equations and Hamiltonian PDEs. This volume presents recent progress in the theory of nonlinear dispersive equations, primarily the nonlinear Schrödinger (NLS) equation. The Cauchy problem for defocusing NLS with critical nonlinearity is discussed. New techniques and results are described on global existence and properties of solutions with large Cauchy data. Current research in harmonic analysis around Strichartz's inequalities and its relevance to nonlinear PDE is presented. Several topics in NLS theory on bounded domains are reviewed. Using the NLS as an example, the book offers comprehensive insight on current research related to dispersive equations and Hamiltonian PDEs. Chapter 1. Introduction And Summary Chapter 2. An Overview Of Results On The Cauchy Problem For Nls Chapter 3. Further Comments Chapter 4. 3d $h^1$-critical Defocusing Nls Chapter 5. Global Wellposedness Below Energy Norm Chapter 6. Nonlinear Schrödinger Equation With Periodic Boundary Conditions Appendix 1. Growth Of Sobolev Norms In Linear Schrödinger Equations With Smooth Time Dependent Potential Appendix 2. Zakharov Systems J. Bourgain. Includes Bibliographical References And Index. Presents the progress in the theory of nonlinear dispersive equations, primarily the nonlinear Schrodinger (NLS) equation. This title discusses the Cauchy problem for defocusing NLS with critical nonlinearity. It also describes various techniques and results on global existence and properties of solutions with large Cauchy data. Presents recent progress in the theory of nonlinear dispersive equations, primarily the nonlinear Schrodinger (NLS) equation. The Cauchy problem for defocusing NLS with critical nonlinearity is discussed and techniques and results are described on global existence