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Vacuum state for spherically symmetric solutions of the compressible Navier-Stokes equations. (English) Zbl 1106.35054

The authors study the properties of vacuum states for a weak solution 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 for the regularity of the velocity excluding the formation of vacuum states is given.

MSC:

35Q30 Navier-Stokes equations
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
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