DISCONTINUOUS SOLUTIONS OF STEADY-STATE, VISCOUS COMPRESSIBLE NAVIER-STOKES EQUATIONS

We study a steady-state, viscous, compressible Navier-Stokes flow in a rectangle Omega = (0, 1) x (-1, 1) with the boundary condition (u, v) = (1, 0) for the velocity field (u, v) and the condition p(0, y) =p(0)(y) for the pressure p on {0} x (-1, 1), which is the part of the boundary where the stream lines emanate. Under the condition that p(0)(y) has a jump at y = 0, we establish the existence and uniqueness of the solution having discontinuity along the stream line starting from the origin. (C) 1995 Academic Press, Inc.