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Analysis of Equilibrium States of Markov Solutions to the 3D Navier-Stokes Equations Driven by Additive Noise

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Abstract

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.

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  1. Dipartimento di Matematica, Università di Firenze, Viale Morgagni 67/a, 50134, Firenze, Italy

    Marco Romito

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  1. Marco Romito
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Correspondence to Marco Romito.

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Romito, M. Analysis of Equilibrium States of Markov Solutions to the 3D Navier-Stokes Equations Driven by Additive Noise. J Stat Phys 131, 415–444 (2008). https://doi.org/10.1007/s10955-007-9477-8

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  • DOI: https://doi.org/10.1007/s10955-007-9477-8

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