Solvability of the problem of the self-propelled motion of several rigid bodies in a viscous incompressible fluid

In this paper, we investigate the problem of the motion of self-propelled rigid bodies in a viscous incompressible fluid filling a bounded container. The motion of the fluid is governed by the Navier–Stokes equations. The bodies move due both to the flow of the ambient fluid and to the engines which are modelled by fluxes of the fluid through the boundaries of the bodies. It is proved that the problem has at least one weak solution on an arbitrary time interval which does not include instants of collisions of the bodies.