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The nonlinear stochastic Schrödinger equation via stochastic Strichartz estimates. (English) Zbl 1401.35257

Summary: We consider the stochastic NLS with nonlinear Stratonovich noise for initial values in \(L^2(\mathbb{R}^d)\) and prove local existence and uniqueness of a mild solution for subcritical and critical nonlinearities. The proof is based on deterministic and stochastic Strichartz estimates. In the subcritical case we prove that the solution is global, if we impose an additional assumption on the nonlinear noise.

MSC:

35Q41 Time-dependent Schrödinger equations and Dirac equations
35R60 PDEs with randomness, stochastic partial differential equations
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60H30 Applications of stochastic analysis (to PDEs, etc.)
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