zbMATH — the first resource for mathematics

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.

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)
Full Text: DOI