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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.


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/1000059519
ISSN: 2365-662X
URN: 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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