We prove that every Markov solution to the three dimensional Navier-Stokes equations with periodic boundary conditions driven by additive Gaussian noise is uniquely ergodic. The convergence to the (unique) invariant measure is exponentially fast. Moreover, we give a well-posedness criterion for the equations in terms of invariant measures. We also analyse the energy balance and identify the term which ensures equality in the balance.
|Titolo:||Analysis of equilibrium states of Markov solutions to the 3D Navier-Stokes equations driven by additive noise|
|Anno del prodotto:||2008|
|Digital Object Identifier (DOI):||10.1007/s10955-007-9477-8|
|Appare nelle tipologie:||1.1 Articolo in rivista|