Analysis of equilibrium states of Markov solutions to the 3D Navier-Stokes equations driven by additive noise

Details Analysis of equilibrium states of Markov solutions to the 3D Navier-Stokes equations driven by additive noise Analysis of equilibrium states of Markov solutions to the 3D Navier-Stokes equations driven by additive noise

2007-09-20

arxiv.org/abs/0709.3267v1

Physics

Mathematical Physics

32 pages

Scientific paper

10.1007/s10955-007-9477-8

We prove that every Markov solution to the three dimensional Navier-Stokes equation 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.

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