Random attractors for stochastic Navier-Stokes equation on a 2D rotating sphere with stable Lévy noise (Q2033861)

The author is interested in the asymptotic behaviour of solutions of the Navier-Stokes equations on 2D rotating spheres perturbed by additive stable Lévy noise. In a prior article \textit{Z. Brzeźniak} et al. [J. Math. Fluid Mech. 20, No. 1, 227--253 (2018; Zbl 1390.35260)] proved the existence of a random (pullback) attractor for these equations with Gaussian noise and sought to extend the results to forcing by stable Lévy process with `heavy-tailed' densities to better capture the possibility of large random inputs with infinite moment. The author takes the view that such noise is more likely to capture stochastic aspects of fluid dynamics at an atomic scale. The article constructs a random dynamical system corresponding to the problem, then establishes the existence of random attractors by investigation of the stationary ergodic solution of an associated Ornstein-Uhlenbeck process, and finally shows the existence of a Feller Markov invariant measure by a corollary of the Markov-Katutani fixed point theorem. The physical implications of these results are not discussed.