Derivative Formula and Applications for Hyperdissipative Stochastic Navier-Stokes/Burgers Equations

TL;DR

This paper establishes a derivative formula for hyperdissipative stochastic Navier-Stokes/Burgers equations using coupling methods, leading to key estimates and properties of the associated Markov semigroup.

Contribution

It introduces a Bismut type derivative formula for these equations and derives several fundamental properties and estimates for the Markov semigroup.

Findings

Gradient estimates derived

Dimension-free Harnack inequality established

Strong Feller property proved

Abstract

By using coupling method, a Bismut type derivative formula is established for the Markov semigroup associated to a class of hyperdissipative stochastic Navier-Stokes/Burgers equations. As applications, gradient estimates, dimension-free Harnack inequality, strong Feller property, heat kernel estimates and some properties of the invariant probability measure are derived.