Stochastic Navier-Stokes equation on a 2D rotating sphere with stable L\'evy noise: existence and uniqueness of weak and strong solutions

TL;DR

This paper establishes the existence and uniqueness of global strong solutions for the stochastic Navier-Stokes equations on a rotating 2D sphere with stable Lévy noise, advancing understanding of stochastic fluid dynamics on curved surfaces.

Contribution

It proves the global existence and uniqueness of strong solutions to stochastic Navier-Stokes equations on a rotating sphere with stable Lévy noise, a novel result in stochastic PDEs on curved manifolds.

Findings

Existence of a unique strong solution globally in time.

Application of stable Lévy noise to model stochastic perturbations.

Extension of stochastic Navier-Stokes theory to spherical geometries.

Abstract

In this paper we prove the existence and uniqueness of a strong solution (in PDE sense) to the stochastic Navier-Stokes equations on the rotating 2-dimensional unit sphere perturbed by stable L\'evy noise. This strong solution turns out to exist globally in time.