Invariance measures of stochastic 2D Navier-Stokes equations driven by $\alpha$-stable processes

TL;DR

This paper establishes the well-posedness and existence of invariant measures for stochastic 2D Navier-Stokes equations driven by general Lévy processes, including α-stable processes, expanding understanding of their long-term behavior.

Contribution

It proves well-posedness and invariant measures for stochastic 2D Navier-Stokes equations driven by Lévy processes, especially α-stable processes, which was not previously known.

Findings

Proved well-posedness of the equations.

Established existence of invariant measures.

Extended results to α-stable Lévy processes.

Abstract

In this note we prove the well-posedness for stochastic 2D Navier-Stokes equation driven by general L\'evy processes (in particular, $\alpha$-stable processes), and obtain the existence of invariant measures.