Local Solutions of a Compressible Flow Problem with Navier Boundary Conditions in General Three-Dimensional Domains

We prove the local-in-time existence of smooth solutions of the Navier–Stokes equations of compressible, barotropic flow posed in a bounded set in R³ with a mixed boundary condition sufficiently general to include the condition proposed by Navier that on the boundary of the spatial domain the velocity should be proportional to the projection of the stress onto the tangent plane.