# Nonlinear Schrödinger equation, differentiation by parts and modulation spaces

Chaichenets, Leonid; Hundertmark, Dirk; Kunstmann, Peer; Pattakos, Nikolaos

Abstract:
We show the local wellposedness of the Cauchy problem for the cubic nonlinear Schrodinger equation in the modulation space M$^{s}$$_{p,q}$(R) where 1 $a \leq \$b q < 3, 2 $a \leq \$b p < 10q0 q0+6 and s $a \geq \$b 0. This improves [7], where the case p = 2 was considered and the dierentiation by parts technique was introduced to a problem with continuous Fourier variable. Here the same technique is used, but more delicate estimates are necessary for p $\neq$ 2.

 Zugehörige Institution(en) am KIT Institut für Analysis (IANA)Sonderforschungsbereich 1173 (SFB 1173) Publikationstyp Forschungsbericht Jahr 2018 Sprache Englisch Identifikator ISSN: 2365-662X URN: urn:nbn:de:swb:90-806812 KITopen ID: 1000080681 Verlag KIT, Karlsruhe Umfang 36 S. Serie CRC 1173 ; 2018/1 Schlagworte nonlinear Schrödinger equation, modulation spaces, wellposedness, differentiation by parts
KIT – Die Forschungsuniversität in der Helmholtz-Gemeinschaft KITopen Landing Page