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

Pattakos, Nikolaos

Abstract:
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.

 Zugehörige Institution(en) am KIT Institut für Analysis (IANA)Sonderforschungsbereich 1173 (SFB 1173) Publikationstyp Forschungsbericht Jahr 2017 Sprache Englisch Identifikator ISSN: 2365-662X URN: urn:nbn:de:swb:90-806485 KITopen ID: 1000080648 Verlag KIT, Karlsruhe Umfang 30 S. Serie CRC 1173 ; 2017/31 Schlagworte nonlinear Schrödinger equation, modulation spaces, wellposedness, differentiation by parts
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