Invariant measure of Burgers' System of equations

Thesis (Ph. D.)--University of Rochester. Dept. of Mathematics, 2009.In this thesis we consider a stochastic version of a system of two equations formulated by Burgers([Burgers, 1954]) with the aim to describe the laminar and turbulent motions of a fluid in a channel. It is shown that there exists a unique invariant measure by proving the boundedness in probability of some solutions and by establishing strong Feller property and irreducibility of the corresponding transition semigroup