Abstract
A class of stochastic 3D Navier-Stokes equation with damping driven by a noise of Lévy type is considered in this paper. The existence and uniqueness of the solution for the problem (1.1)–(1.2) are proved for β>2 with any α>0 and α≥14 as β=2. The main result covered various types of SPDE such as stochastic 3D Navier-Stokes equations with damping, stochastic tamed 3D Navier-Stokes equations, stochastic three-dimensional Brinkman-Forchheimer-extended Darcy model. By using the exponential stability of solutions, the existence of a unique invariant measures is proved.
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