Exponential Mixing of the 3D Stochastic Navier-Stokes Equations Driven by Mildly Degenerate Noises

Albeverio S; Debussche A; Xu LH

Applied Mathematics and Optimization, Vol.66, No.2, 273-308, 2012

DOI10.1007/s00245-012-9172-2 Export Citation

Exponential Mixing of the 3D Stochastic Navier-Stokes Equations Driven by Mildly Degenerate Noises

We prove the strong Feller property and exponential mixing for 3D stochastic Navier-Stokes equation driven by mildly degenerate noises (i.e. all but finitely many Fourier modes being forced) via a Kolmogorov equation approach.

Keywords:3D stochastic Navier-Stokes equation (SNS);Kolmogorov equation;Galerkin approximation;Strong Feller;Exponential mixing;Mildly degenerate noises;Malliavin calculus