Dynamics of the density discontinuity interface. A transversal contact problem
Abstract: The Navier–Stokes equations for the motion of compressible, viscous fluids in the half-space R+2 with the no-slip boundary condition are considered. We study the problem of determining the evolution of the interface of discontinuity of a piece-wise W1,p, p>2, density when the interface is in transversal contact with the boundary of the domain. A unique global solution that exists near a constant equilibrium case is constructed that preserves C1+α regularity of the interface.