In this paper we prove that the stochastic Navier-Stokes equations with stable Lévy noise generate a random dynamical systems. Then existence of attractor for on 2D spheres under (finite dimensional). We also deduce Feller Markov Invariant Measure.

We construct extremal stochastic integrals ∫ e E f(u)Mα(du) of a deterministic function f(u) ≥ 0 with respect to a random α−Fréchet (α > 0) sup–measure. The measure Mα is sup–additive rather than additive and is defined over a general measure space (E, E , μ), where μ is a deterministic control measure. The extremal integral is constructed in a way similar to the usual α−stable integral, but wi...