On self-similar solutions to degenerate compressible Navier-Stokes equations (Q2658931)

The authors consider the compressible Navier-Stokes-Fourier system in multiple dimensions (\(d \geq 3\)) for heat-conducting Newtonian gases. The problem is in the whole space, thus is a Cauchy problem. The system is studied near the vacuum. The focus is on radially-symmetrical and self-similar solutions. The authors assume that the solutions exhibit cavitation at the origin. Solutions are of two types: expanders and shrinkers. Existence of the former and impossibility of the latter are proved, both assumed to be small.