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.

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

ROMITO, MARCO
2008-01-01

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.
2008
Romito, Marco
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/121737
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