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DOI: 10.5445/IR/1000072001

Martingale solutions for the stochastic nonlinear Schrödinger equation in the energy space

Brzezniak, Zdzislaw; Hornung, Fabian; Weis, Lutz

Abstract:
We consider a stochastic nonlinear Schrödinger equation with multiplicative noise in an abstract framework that covers subcritical focusing and defocusing Stochastic NLSE in H¹ on compact manifolds and bounded domains. We construct a martingale solution using a modified Faedo-Galerkin-method based on the Littlewood-Paley-decomposition. For 2d manifolds with bounded geometry, we use Strichartz estimates to show pathwise uniqueness.


Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht
Jahr 2017
Sprache Englisch
Identifikator ISSN: 2365-662X
URN: urn:nbn:de:swb:90-720011
KITopen ID: 1000072001
Verlag KIT, Karlsruhe
Umfang 51 S.
Serie CRC 1173 ; 2017/18
Schlagworte nonlinear Schrödinger equation, multiplicative noise, Galerkin approximation, compactness method
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