Global solutions to compressible Navier-Stokes equations with spherical symmetry and free boundary

This work is devoted to study the global existence of strong and classical solutions to the compressible Navier-Stokes equations with or without a density jump on the moving boundary for the spherically symmetric motion. We establish a unified method to track the propagation of regularity of strong and classical solutions which works for the cases when the density connects to vacuum continuously and with a jump simultaneously. The result we obtain is able to deal with both strong solutions with physical vacuum for which the sound speed is 1∕2-Hölder continuous across the boundary, and classical solutions with physical vacuum when 1<γ<3. In contrast to the previous results of global weak solutions, we track the regularity globally-in-time up to the symmetry centre and the moving boundary. In particular, the free boundary can be traced.