  The Vlasov equation models a group of particles moving under a potential $V$;
moreover, each particle exerts a force, of potential $W$, on the other ones. We
shall suppose that these particles move on the $p$-dimensional torus ${\bf
T}^p$ and that the interaction potential $W$ is smooth. We are going to perturb
this equation by a Brownian motion on ${\bf T}^p$; adapting to the viscous case
methods of Gangbo, Nguyen, Tudorascu and Gomes, we study the existence of
periodic solutions and the asymptotics of the Hopf-Lax semigroup.
