TY  - BOOK
AU  - Koch,Herbert
AU  - Tataru,Daniel
AU  - Vişan,Monica
ED  - SpringerLink (Online service)
TI  - Dispersive Equations and Nonlinear Waves: Generalized Korteweg–de Vries, Nonlinear Schrödinger, Wave and Schrödinger Maps 
T2  - Oberwolfach Seminars,
SN  - 9783034807364
AV  - QA370-380 
U1  - 515.353 23
PY  - 2014///
CY  - Basel
PB  - Springer Basel, Imprint: Birkhäuser
KW  - Mathematics
KW  - Partial differential equations
KW  - Partial Differential Equations
KW  - Electronic books
KW  - local
N2  - The first part of the book provides an introduction to key tools and techniques in dispersive equations: Strichartz estimates, bilinear estimates, modulation and adapted function spaces, with an application to the generalized Korteweg-de Vries equation and the Kadomtsev-Petviashvili equation. The energy-critical nonlinear Schrödinger equation, global solutions to the defocusing problem, and scattering are the focus of the second part. Using this concrete example, it walks the reader through the induction on energy technique, which has become the essential methodology for tackling large data critical problems. This includes refined/inverse Strichartz estimates, the existence and almost periodicity of minimal blow up solutions, and the development of long-time Strichartz inequalities. The third part describes wave and Schrödinger maps. Starting by building heuristics about multilinear estimates, it provides a detailed outline of this very active area of geometric/dispersive PDE. It focuses on concepts and ideas and should provide graduate students with a stepping stone to this exciting direction of research
UR  - http://ezproxy.alfaisal.edu/login?url=http://dx.doi.org/10.1007/978-3-0348-0736-4
ER  -