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Existence result for the motion of several rigid bodies in an incompressible non-Newtonian fluid with growth conditions in Orlicz spaces

We prove the existence of weak solutions to the problem of the motion of one or several rigid bodies immersed in a non-Newtonian fluid of rheology more general than power-law. The nonlinear viscous term in the equation is described with the help of a general convex function defining Orlicz spaces. The main ingredient of the proof is the convergence of the nonlinear term achieved with the help of pressure localization and monotonicity methods.