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On stochastic evolution equations for nonlinear bipolar fluids: well-posedness and some properties of the solution. (English) Zbl 1383.35161
Summary: 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 $$L^2$$.

##### MSC:
 35Q35 PDEs in connection with fluid mechanics 35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs 35R60 PDEs with randomness, stochastic partial differential equations
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