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NLS in the modulation space M$_{2,q}$

Pattakos, Nikolaos


We show the local wellposedness of the Cauchy problem for the cubic nonlinear Schrödinger equation in the modulation space M$^{s}$ $_{2,q}$(R), 1 $a \leq \ $b q < 3 and s $a \geq \ $b 0. This improves [3] (for 2 $a \leq \ $b q < 3) where the cases 2 $a \leq \ $b q < unendlich were considered but the solution given there was not persistent. It is done with the use of the differentiation by parts technique and it is the first time that this purely periodic tool is used to attack a problem with a continuous Fourier variable.

Volltext §
DOI: 10.5445/IR/1000080648
Veröffentlicht am 01.03.2018
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsjahr 2017
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000080648
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 30 S.
Serie CRC 1173 ; 2017/31
Schlagwörter nonlinear Schrödinger equation, modulation spaces, wellposedness, differentiation by parts
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