Talagrand's transportation inequality for SPDEs with locally monotone drifts

Abstract

The purpose of this paper is twofold. Firstly, we prove transportation inequalities \({\bf T_2}(C)\) on the space of continuous paths with respect to the uniform metric for the law of the solution to a class of non-linear monotone stochastic partial differential equations (SPDEs) driven by the Wiener noise. Furthermore, we also establish the \({\bf T_1}(C)\) property for such SPDEs but with merely locally monotone coefficients, including the stochastic Burgers type equation and stochastic \(2\)-D Navier-Stokes equation.