Abstract
We consider a stochastic model for the motion of an incompressible isothermal mixture of two immiscible non-Newtonian fluids perturbed by a multiplicative noise of Gaussian and Levy type. The model consists of the stochastic Oldroyd model of order one, coupled with a stochastic nonlocal Cahn-Hilliard model. Global existence and uniqueness of strong probabilistic solution is established. Moreover, we show that the sequence of Galerkin approximation converges in mean square to the exact strong probabilistic solution of the problem.
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