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In this paper we prove the existence and uniqueness of a strong solution (inPDE sense) to the stochastic Navier-Stokes equations on the rotating2-dimensional unit sphere perturbed by stable L\'evy noise. This strongsolution turns out to exist globally in time.

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