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Ergodicity of the finite-dimensional approximation of the 3D Navier-Stokes equations forced by a degenerate noise. (English) Zbl 1060.76027
Summary: We prove ergodicity of finite-dimensional approximations of 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.

MSC:
76D06 Statistical solutions of Navier-Stokes and related equations
76M35 Stochastic analysis applied to problems in fluid mechanics
35Q30 Navier-Stokes equations
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
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