# Invariant measures for the Stochastic Navier-Stokes equation on a 2D rotating sphere with stable L\'evy noise

## TL;DR

This paper proves the existence of invariant measures for the 2D stochastic Navier-Stokes equations on a rotating sphere driven by stable Lévy noise, extending previous well-posedness results.

## Contribution

It establishes the existence of invariant measures under finite-dimensional Lévy noise, advancing understanding of stochastic fluid dynamics on curved surfaces.

## Key findings

- Invariant measures exist for the stochastic Navier-Stokes equations on a sphere.
- The proof relies on finite-dimensional Lévy noise assumptions.
- Extends previous well-posedness results to invariant measure existence.

## Abstract

Building upon the well-posedness results in \cite{snse1}, in this note we prove the existence of invariant measures for the stochastic Navier-Stokes equations with stable L\'evy noise. The crux of our proof relies on the assumption of finite dimensional L\'evy noise.