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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.
Xin et al. (2006) studied this question.