Cauchy problem for non-autonomous Navier-Stokes equations in an unbounded domain

This paper concerns the global existence of solutions to a system of non-linear compressible non-autonomous Navier-Stokes equations in an unbounded domain. To prove the global existence, we first study an approximate problem in a bounded domain and obtain a priori estimates independent of the boundary of the domain. Then letting the diameter of the domain tend to infinity, we get a global spherically symmetric solution as the limit.