GLOBAL SOLVABILITY AND VANISHING SHEAR VISCOSITY LIMIT FOR A SIMPLIFIED COMPRESSIBLE NAVIER-STOKES SYSTEM WITH TEMPERATURE-DEPENDENT VISCOSITY

We consider the nonhomogeneous initial boundary value problem for a simplified compressible Navier-Stokes system with cylindrical symmetry and temperature-dependent viscosity, in which the acceleration effect in one direction is ignored. The global unique solvability of strong solution with large data is proved, the vanishing shear viscosity limit is justified, and the optimal L-2 convergence rate for the angular and axial velocities is obtained together with the estimation on the boundary layer thickness. The results are proved by establishing some (shear viscosity-independent) a priori estimates that are based on the basic energy estimates as well as the upper and lower bounds of the density. First, the basic energy estimates are derived by a new strategy used to overcome the difficulties caused by the loss of time derivative of one-direction velocity and the nonhomogeneous boundary conditions, and then the bounds of the density based on a key observation of the structure of the viscosities.