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Local existence and non-explosion of solutions for stochastic fractional partial differential equations driven by multiplicative noise. (English) Zbl 1329.60220
Summary: In this paper, we prove the local existence and uniqueness of solutions for a class of stochastic fractional partial differential equations driven by multiplicative noise. We also establish that for this class of equations adding linear multiplicative noise provides a regularizing effect: the solutions will not blow up with high probability if the initial data is sufficiently small, or if the noise coefficient is sufficiently large. As applications, our main results are applied to various types of SPDEs such as stochastic reaction-diffusion equations, stochastic fractional Burgers equation, stochastic fractional Navier-Stokes equation, stochastic quasi-geostrophic equations and stochastic surface growth PDEs.

MSC:
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60H30 Applications of stochastic analysis (to PDEs, etc.)
35R60 PDEs with randomness, stochastic partial differential equations
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