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On existence of global solutions of the one-dimensional cubic NLS for initial data in the modulation space Mp,q(R)

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

Abstract:
We prove global existence for the one-dimensional cubic non-linear Schrödinger equation in modulation spaces Mp,p' for p sufficiently close to 2. In contrast to known results, [9] and [14], our result requires no smallness condition on initial data. The proof adapts a splitting method inspired by work of Vargas-Vega, Hyakuna-Tsutsumi and Grünrock to the modulation space setting and exploits polynomial growth of the free Schödinger group on modulation spaces.

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Volltext §
DOI: 10.5445/IR/1000059519
Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht
Jahr 2016
Sprache Englisch
Identifikator ISSN: 2365-662X
urn:nbn:de:swb:90-595199
KITopen-ID: 1000059519
Verlag KIT, Karlsruhe
Umfang 13 S.
Serie CRC 1173 ; 2016/21
Schlagworte nonlinear Schrödinger equation, global solutions, modulation spaces, infinite mass solutions
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