Explicit Solutions for the Semi-Stationary Compressible Stokes Problem

In this paper, we present some explicit solutions for the 2D and 3D semi-stationary compressible Stokes problem, which is a gross simplification of the isentropic compressible Navier-Stokes equations. For the explicit solutions, the density is a function of time which decreases to zero at an exponential rate and the velocity is a combination of a time function and a quadratic polynomial with respect to the space variables.