On stochastic evolution equations for nonlinear bipolar fluids: Well-posedness and some properties of the solution

We investigate the stochastic evolution equations describing the motion of a non-Newtonian fluids excited by multiplicative noise of Lévy type. We show that the system we consider has a unique global strong solution. We also give some results concerning the properties of the solution. We mainly prove that the unique solution satisfies the Markov–Feller property. This enables us to prove by means of some results from ergodic theory that the semigroup associated to the unique solution admits at least an invariant measure which is ergodic and tight on a subspace of the Lebesgue space L2L2.