Well-posedness and large deviation principle for a class of SPDEs

Abstract

In this paper, we study a class of stochastic partial differential equations with general locally monotone coefficients under thevariational framework. By proving the existence of martingale solutions and pathwise uniqueness, we first get the existence and uniqueness of strong solutions. Then we prove the large deviation principle by using the stochastic control and weakconvergence approach. The mainresults are applicable to various concrete SPDE models, such as stochastic Cahn-Hilliard equation, stochastic Kuramoto-Sivashinsky equation and stochastic 3D tamedNavier-Stokes equation.