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Ergodicity of the finite dimensional approximation of the 3D Navier-Stokes equations forced by a degenerate noise

M. Romito
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Abstract

We prove ergodicity of the finite dimensional approximations of the three dimensional Navier-Stokes equations, driven by a random force. The forcing noise acts only on a few modes and some algebraic conditions on the forced modes are found that imply the ergodicity. The convergence rate to the unique invariant measure is shown to be exponential.

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M. Romito. 2002-10-05. Ergodicity of the finite dimensional approximation of the 3D Navier-Stokes equations forced by a degenerate noise. https://arxiv.org/abs/math/0210082

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