Abstract:
One of the cleanest mathematical models of two-dimensional
turbulence are the stochastic Navier-Stokes equations. We give
sufficient (and in some sense close to necessary) conditions on the
covariance of the driving force to obtain the uniqueness of the
stationary state of these equations. It can be shown that under
these conditions, the convergence in law of arbitrary solutions to
the stationary one is exponential. We are furthermore able to
exhibit a space of observables in which the generator of the
dynamics has a spectral gap.