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The nonlinear stochastic Schrödinger equation via stochastic Strichartz estimates

Hornung, Fabian

Abstract:
We consider the stochastic NLS with linear multiplicative noise in L2(Rd) and prove the existence and uniqueness of a global solution in the subcritical and a local solution in the critical case, respectively. In particular, we relax the regularity assumptions on the noise from Barbu, R¨ockner and Zhang (Stochastic Nonlinear Schr¨odinger Equations with Linear Multiplicative Noise: Rescaling Approach. Journal of Nonlinear Science 24(3):383-409,2014). The proof is based on deterministic and stochastic Strichartz estimates.


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/1000062309
ISSN: 2365-662X
URN: urn:nbn:de:swb:90-623092
KITopen ID: 1000062309
Verlag KIT, Karlsruhe
Umfang 19 S.
Serie CRC 1173 ; 2016/32
Schlagworte nonlinear Schrödinger equation, Stratonovich noise, stochastic Strichartz estimates
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