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DOI: 10.5445/IR/1000080681

Nonlinear Schrödinger equation, differentiation by parts and modulation spaces

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

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
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