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

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.