Strong solutions for the stochastic Navier-Stokes equations on the 2D rotating sphere with stable Lévy noise

Abstract

The Navier-Stokes equation with rough data arises in many problems of fluid dynamics but mathematical analysis of such problems is notoriously difficult. In this paper we consider a two-dimensional fluid moving on the surface of a rotating sphere under the influence of an impulsive force that is very irregular in time. More precisely, we assume that the impulsive force is associated to a Brownian Motion subordinated by a stable subordinator. Then 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 a stable Lévy noise. This strong solution turns out to exist globally in time.