On the zero-velocity-limit solutions to the Navier-Stokes equations of compressible flow

We consider the zero-velocity stationary problem of the Navier-Stokes equations of compressible isentropic flow describing the distribution of the density rho of a fluid in a spatial domain Omega subset of R-N driven by a time independent potential external force f = del F. A sharp condition in terms of F is given for the problem to possess a unique nonnegative solution rho having a prescribed mass m > 0.