  We study a model of the motion by mean curvature of an (1+1) dimensional
interface in a 2D Brownian velocity field. For the well-posedness of the model
we prove existence and uniqueness for certain degenerate nonlinear stochastic
evolution equations in the variational framework of Krylov Rozovskii, replacing
the standard coercivity assumption by a Lyapunov type condition. Ergodicity is
established for the case of additive noise, using the lower bound technique for
Markov semigroups by Komorowski, Peszat and Szarek
