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

TL;DR

This paper proves that the 3D stochastic Navier-Stokes equations with mildly degenerate noise exhibit exponential mixing and the strong Feller property, advancing understanding of their long-term statistical behavior.

Contribution

It establishes exponential mixing and the strong Feller property for 3D stochastic Navier-Stokes equations driven by mildly degenerate noises using a Kolmogorov equation approach.

Findings

Proves exponential mixing for the equations.

Demonstrates the strong Feller property.

Uses Kolmogorov equation method for analysis.

Abstract

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.