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Ergodic properties of highly degenerate 2D stochastic Navier-Stokes equations. (English) Zbl 1059.60073
Summary: This note presents the results from “Ergodicity of the degenerate stochastic 2D Navier-Stokes equation” (to appear) by the authors. We study the Navier-Stokes equation on the two-dimensional torus when forced by a finite-dimensional Gaussian white noise and give conditions under which the system is ergodic. In particular, our results hold for specific choices of four-dimensional Gaussian white noise.

MSC:
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
76D05 Navier-Stokes equations for incompressible viscous fluids
35Q30 Navier-Stokes equations
37L55 Infinite-dimensional random dynamical systems; stochastic equations
76M35 Stochastic analysis applied to problems in fluid mechanics
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