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 L\'evy type. By making use of Galerkin approximation we can prove that the system has a global (probabilistic) strong solution. This solution is unique and we also prove that the sequence of Galerkin solution converges to this unique solution in mean square.