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In this paper we prove the local existence and uniqueness of solutions for aclass of stochastic fractional partial differential equations driven bymultiplicative noise. We also establish that for this class of equations addinglinear multiplicative noise provides a regularizing effect: the solutions willnot blow up with high probability if the initial data is sufficiently small, orif the noise coefficient is sufficiently large. As applications our mainresults are applied to various types of SPDE such as stochasticreaction-diffusion equations, stochastic fractional Burgers equation,stochastic fractional Navier-Stokes equation, stochastic quasi-geostrophicequations and stochastic surface growth PDE.

Local existence and non-explosion of solutions for stochastic fractional partial differential equations driven by multiplicative noise