Lᵖ-theory for strong solutions to fluid-rigid body interaction in Newtonian and generalized Newtonian fluids

Consider the system of equations describing the motion of a rigid body immersed in a viscous, incompressible fluid of Newtonian or generalized Newtonian type. The class of fluids considered includes in particular shear-thinning or shear-thickening fluids of power-law type of exponent d≥ 1. We develop a method to prove that this system admits a unique, local, strong solution in the Lᵖ-setting. The approach presented in the case of generalized Newtonian fluids is based on the theory of quasi-linear evolution equations and requires that the exponent p satisfies the condition $p>5$.