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

Abstract

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 SPDE such as stochastic reaction-diffusion equations, stochastic fractional Burgers equation, stochastic fractional Navier-Stokes equation, stochastic quasi-geostrophic equations and stochastic surface growth PDE.