VACUUM STATE FOR SPHERICALLY SYMMETRIC SOLUTIONS OF THE COMPRESSIBLE NAVIER–STOKES EQUATIONS

We study the properties of vacuum states in weak solutions to the compressible Navier–Stokes system with spherical symmetry. It is shown that vacuum states cannot develop later on in time in a region far away from the center of symmetry, provided there is no vacuum state initially and two initially non-interacting vacuum regions never meet each other in the future. Furthermore, a sufficient condition on the regularity of the velocity excluding the formation of vacuum states is given.