Boundary geometry and regularity of solution to the compressible Navier-Stokes equations in bounded domains of R-n

Abstract

We study the barotropic compressible Navier-Stokes equations in a bounded domain of R-n. Nonzero velocities are prescribed on the boundary of Q and the density is assigned on that part of the boundary corresponding to entering velocity. We show that some geometries of the boundaries near the junctions of inflow and outflow boundaries can generate mild singularities in the solution. Existence of solution to the nonlinear equations is shown by the Schauder fixed point theory. (c) 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim