Rotationally symmetric viscous gas flows

The Dirichlet boundary value problem for the Navier–Stokes equations of a barotropic viscous compressible fluid is considered. The flow region and the data of the problem are assumed to be invariant under rotations about a fixed axis. The existence of rotationally symmetric weak solutions for all adiabatic exponents from the interval $(\gamma^*, \infty)$ with a critical exponent $\gamma^*< 4/3$ is proved.