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Localwell-posedness for the nonlinear Schrödinger equation in modulation spaces Ms p;q(Rd)

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

Abstract:
We show the local well-posedness of the Cauchy problem for the cubic nonlinear Schrödinger equation on modulation spaces Msp;q(Rd) for d 2 N, 1 p; q 1 and s > d 1 􀀀 1 q for q > 1 or s 0 for q = 1. This improves [4, Theorem 1.1] by Bényi and Okoudjou where only the case q = 1 is considered. Our result is based on the algebra property of modulation spaces with indices as above for which we give an elementary proof via a new Hölder-like inequality for modulation spaces.


Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht
Jahr 2016
Sprache Englisch
Identifikator DOI(KIT): 10.5445/IR/1000061425
ISSN: 2365-662X
URN: urn:nbn:de:swb:90-614256
KITopen ID: 1000061425
Verlag KIT, Karlsruhe
Umfang 10 S.
Serie CRC 1173 ; 2016/30
Schlagworte modulation spaces, nonlinear Schrödinger equation, local well-posedness
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