Fluids in the exterior domain of several moving obstacles

Recently, the question of solvability and possible uniqueness of solutions to the Navier-Stokes equations in the exterior domain of several moving obstacles gained quite some attention. We consider both Newtonian and a large class of non-Newtonian fluids in this setting and prove the existence of a locally in time existing strong Lp-solution to the fundamental system of equations in fluid dynamics. Our method is based on a suitable transform allowing to consider an equivalent system on a cylindrical geometry and we use results about maximal Lp-regularity of operators in certain function spaces. This approach can be applied successfully for both shear thickening and shear thinning fluids. Furthermore, we compare different classes of solutions, such as mild, strong and very weak solutions.