Global Solutions to Compressible Navier-Stokes Equations With Spherically Symmetric Motion and Free Boundary

This work is devoted to study the global existence of strong and classical solutions to compressible Navier-Stokes equations with or without density jump on the moving boundary for 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 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 $1/2$-H\"older continuous across the boundary, and classical solutions with physical vacuum when $1 < \gamma < 3$. In contrast to the previous results of global weak solutions, we track the regularity globally-in-time up to the symmetric center and the moving boundary. In particular, the free boundary can be traced.