Stability of three-dimensional stochastic Navier-Stokes equation with Markov switching

TL;DR

This paper investigates the stability properties of a 3D stochastic Navier-Stokes equation incorporating Markov switching in the noise, providing insights into its exponential stability under stochastic influences.

Contribution

It introduces a novel stochastic Navier-Stokes model with Markov switching and analyzes its moment and almost sure exponential stability.

Findings

Established $p$-th moment exponential stability.

Proved almost surely exponential stability.

Extended stability analysis to stochastic Navier-Stokes with Markov switching.

Abstract

A right continuous Markov chain is introduced in the noise terms of the three-dimensional stochastic Navier-Stokes equation, and we call such stochastic system as stochastic Navier-Stokes equation with Markov switching. In the present article, we study the $p$-th moment exponential stability and the almost surely exponential stability of the solution to the equation.