The Motion of a Solid Body in a Viscous Incompressible Fluid under the Action of External and Hydrodynamic Forces and Momenta

摘要

We consider a joint initial-boundary value problem about the motion of a solid body and a viscous incompressible fluid in a bounded three-dimensional domain under the action of a given force and a given momentum with hydrodynamic reactions taken into account. We use the existence and uniqueness theorem for the generalized solution of the Navier-Stokes equations in a domain with a given motion on the boundary [1,2] supplemented by a theorem on a solenoidal time-differ-entiable extension of a vector field from the boundary of a domain [3], The smoothness assumption on the solution [1,2] makes it possible to prove the unique solvability of the initial problem by reducing it to the Cauchy problem for a system of ordinary differential equations.