000 02370nam a22003738i 4500
001 CR9781108590518
003 UkCbUP
005 20200124160156.0
006 m|||||o||d||||||||
007 cr||||||||||||
008 171221s2019||||enk o ||1 0|eng|d
020 _a9781108590518 (ebook)
020 _z9781108472081 (hardback)
040 _aUkCbUP
_beng
_erda
_cUkCbUP
050 0 0 _aQC174.26.W28
_bD63 2019
082 0 0 _a530.12/4
_223
100 1 _aDodson, Benjamin,
_d1983-
_eauthor.
245 1 0 _aDefocusing nonlinear Schrödinger equations /
_cBenjamin Dodson.
264 1 _aCambridge :
_bCambridge University Press,
_c2019.
300 _a1 online resource (xii, 242 pages) :
_bdigital, PDF file(s).
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
490 1 _aCambridge tracts in mathematics ;
_v217
500 _aTitle from publisher's bibliographic system (viewed on 22 Mar 2019).
505 0 _aA 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.
520 _aThis 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.
650 0 _aGross-Pitaevskii equations.
650 0 _aSchrödinger equation.
650 0 _aDifferential equations, Nonlinear.
776 0 8 _iPrint version:
_z9781108472081
830 0 _aCambridge tracts in mathematics ;
_v217.
856 4 0 _uhttps://www.cambridge.org/core/product/identifier/9781108590518/type/BOOK
999 _c514491
_d514489