TY  - BOOK
AU  - Dodson,Benjamin
TI  - Defocusing nonlinear Schrödinger equations
T2  - Cambridge tracts in mathematics
SN  - 9781108590518 (ebook)
AV  - QC174.26.W28 D63 2019
U1  - 530.12/4 23
PY  - 2019///
CY  - Cambridge
PB  - Cambridge University Press
KW  - Gross-Pitaevskii equations
KW  - Schrödinger equation
KW  - Differential equations, Nonlinear
N1  - Title from publisher's bibliographic system (viewed on 22 Mar 2019); A first look at the mass-critical problem -- The cubic NLS in dimensions three and four -- The energy-critical problem in higher dimensions -- Mass-critical NLS problem in higher dimensions -- Low-dimensional well-posedness results
N2  - This study of Schrödinger equations with power-type nonlinearity provides a great deal of insight into other dispersive partial differential equations and geometric partial differential equations. It presents important proofs, using tools from harmonic analysis, microlocal analysis, functional analysis, and topology. This includes a new proof of Keel-Tao endpoint Strichartz estimates, and a new proof of Bourgain's result for radial, energy-critical NLS. It also provides a detailed presentation of scattering results for energy-critical and mass-critical equations. This book is suitable as the basis for a one-semester course, and serves as a useful introduction to nonlinear Schrödinger equations for those with a background in harmonic analysis, functional analysis, and partial differential equations
UR  - https://www.cambridge.org/core/product/identifier/9781108590518/type/BOOK
ER  -