M-Dissipativity for Kolmogorov Operator of a Fractional Burgers Equation with Space-time White Noise

Abstract

This paper is concerned with the essential m-dissipativity of the Kolmogorov operator associated with a fractional stochastic Burgers equation with space-time white noise. Some estimates on the solution and its moments with respect to the invariant measure are given. Moreover we also study the smoothing properties of the transition semigroup and the corresponding fractional Ornstein-Uhlenbeck operator by introducing an auxiliary semigroup and (generalized) Bismut-Elworthy formula. From these results, we prove that the Kolmogorov operator of the problem is m-dissipative and the domain of the infinitesimal generator of the fractional Ornstein-Uhlenbeck operator is a core.