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

Brzezniak, Zdzislaw; Hornung, Fabian; Weis, Lutz

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.

Volltext §
DOI: 10.5445/IR/1000072001
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsjahr 2017
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000072001
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 51 S.
Serie CRC 1173 ; 2017/18
Schlagwörter nonlinear Schrödinger equation, multiplicative noise, Galerkin approximation, compactness method
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