SOLUTIONS IN LEBESGUE SPACES OF THE NAVIER-STOKES EQUATIONS WITH DYNAMIC BOUNDARY-CONDITIONS

This paper, although self-contained, is a continuation of the work don e in [8], where the motion of a viscous, incompressible fluid is consi dered in conjunction with the rotation of a rigid body which is immers ed in the fluid. The resulting mathematical model is a Navier-Stokes p roblem with dynamic boundary conditions. In [8] a unique L2,3 solution is constructed under certain regularity assumptions on the initial st ates. In this paper we consider the Navier-Stokes problem with dynamic boundary conditions in the Lebesgue spaces L(r,3) (3 < r < infinity) and prove the existence of a unique solution, local in time, without i mposing any regularity conditions on the initial states.