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arXiv · 0709.3267

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

Marco Romito
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Abstract

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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Marco Romito. 2007-09-20. Analysis of equilibrium states of Markov solutions to the 3D Navier-Stokes equations driven by additive noise. https://doi.org/10.1007/s10955-007-9477-8

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