LEADER 03754nam 22006615 450 001 9910299976903321 005 20250609110059.0 010 $a3-0348-0736-8 024 7 $a10.1007/978-3-0348-0736-4 035 $a(CKB)3710000000212205 035 $a(Springer)9783034807364 035 $a(MH)014131694-2 035 $a(SSID)ssj0001296458 035 $a(PQKBManifestationID)11721671 035 $a(PQKBTitleCode)TC0001296458 035 $a(PQKBWorkID)11347690 035 $a(PQKB)11201961 035 $a(DE-He213)978-3-0348-0736-4 035 $a(MiAaPQ)EBC6314607 035 $a(MiAaPQ)EBC5586448 035 $a(Au-PeEL)EBL5586448 035 $a(OCoLC)1066184980 035 $a(PPN)179927000 035 $a(MiAaPQ)EBC1783840 035 $a(EXLCZ)993710000000212205 100 $a20140714d2014 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aDispersive Equations and Nonlinear Waves $eGeneralized Korteweg?de Vries, Nonlinear Schrödinger, Wave and Schrödinger Maps /$fby Herbert Koch, Daniel Tataru, Monica Vi?an 205 $a1st ed. 2014. 210 1$aBasel :$cSpringer Basel :$cImprint: Birkhäuser,$d2014. 215 $a1 online resource (XII, 312 p. 1 illus.)$conline resource 225 1 $aOberwolfach Seminars,$x1661-237X ;$v45 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a3-0348-0735-X 320 $aIncludes bibliographical references (pages [309]-312). 330 $aThe first part of the book provides an introduction to key tools and techniques in dispersive equations: Strichartz estimates, bilinear estimates, modulation and adapted function spaces, with an application to the generalized Korteweg-de Vries equation and the Kadomtsev-Petviashvili equation. The energy-critical nonlinear Schrödinger equation, global solutions to the defocusing problem, and scattering are the focus of the second part. Using this concrete example, it walks the reader through the induction on energy technique, which has become the essential methodology for tackling large data critical problems. This includes refined/inverse Strichartz estimates, the existence and almost periodicity of minimal blow up solutions, and the development of long-time Strichartz inequalities. The third part describes wave and Schrödinger maps. Starting by building heuristics about multilinear estimates, it provides a detailed outline of this very active area of geometric/dispersive PDE. It focuses on concepts and ideas and should provide graduate students with a stepping stone to this exciting direction of research. 410 0$aOberwolfach Seminars,$x1661-237X ;$v45 606 $aDifferential equations, Partial 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 615 0$aDifferential equations, Partial. 615 14$aPartial Differential Equations. 676 $a515.355 676 $a530.124 700 $aKoch$b Herbert$4aut$4http://id.loc.gov/vocabulary/relators/aut$036792 702 $aTataru$b Daniel$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aVi?an$b Monica$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299976903321 996 $aDispersive Equations and Nonlinear Waves$92541504 997 $aUNINA 999 $aThis Record contains information from the Harvard Library Bibliographic Dataset, which is provided by the Harvard Library under its Bibliographic Dataset Use Terms and includes data made available by, among others the Library of Congress