Exponential mixing of the 3D stochastic Navier-Stokes equations driven by mildly degenerate noises

Sergio Albeverio (1) , Arnaud Debussche (2, 3) , Lihu Xu (4)

1 HCM - Hausdorff Center for Mathematics
2 IPSO - Invariant Preserving SOlvers
3 IRMAR - Institut de Recherche Mathématique de Rennes
4 EURANDOM - European Institute for Statistics, Probability, Stochastic Operations Research and its Applications

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 are forced) via Kolmogorov equation approach.

Mots clés: stochastic Navier-Stokes equation (SNS); Kolmogorov equation; Galerkin approximation; strong Feller; exponential mixing; mildly degenerate noise; Malliavin calculus

Domaines: Equations aux dérivées partielles [math.AP]; Probabilités [math.PR]

Sergio Albeverio, Arnaud Debussche, Lihu Xu. Exponential mixing of the 3D stochastic Navier-Stokes equations driven by mildly degenerate noises. Applied Mathematics and Optimization, 2012, 66 (2), pp.273-308. ⟨10.1007/s00245-012-9172-2⟩. ⟨hal-00463793⟩