On the slow motion of a self-propelled rigid body in a viscous incompressible fluid

AbstractIn this paper we study the Stokes approximation of the self-propelled motion of a rigid body in a viscous liquid that fills all the three-dimensional space exterior to the body. We prove the existence and uniqueness of strong solution to the coupled systems of equations describing the motion of the system body–liquid, for any time and any regular distribution of velocity on the boundary of the body. For the corresponding stationary problem we derive Lp-estimates for the solution in terms of the data. Finally, we prove that every steady solution is attainable as the limit, when t→∞, of an unsteady self-propelled solution which starts from rest