  We consider a stochastic electroconvection model describing the nonlinear
evolution of a surface charge density in a two-dimensional fluid with additive
stochastic forcing. We prove the existence and uniqueness of solutions, we
define the corresponding Markov semigroup, and we study its Feller properties.
When the noise forces enough modes in phase space, we obtain the uniqueness of
the smooth invariant measure for the Markov transition kernels associated with
the model.
