Long-time behaviour of the 2D stochastic Navier-Stokes equations
Martin Hairer, University of Warwick

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.