COMPRESSIBLE NAVIER-STOKES EQUATIONS IN A BOUNDED DOMAIN WITH INFLOW BOUNDARY-CONDITION

In this paper, we study the barotropic compressible Navier-Stokes equa tions in a bounded plane domain Omega. Nonzero velocities are prescrib ed on the boundary of Omega, and the density is prescribed on that par t of the boundary corresponding to entering velocity. This causes a we ak singularity in the solution at the junction of incoming and outgoin g flows. We prove the existence of the solution (U, p) of the system [ GRAPHICS] in the Sobolev space H-2,H-q x H-1,H-q(2 < q < 3). The proof follows from an analysis of the linearized problem and a fixed-point argument.