Global well-posedness for the compressible Navier-Stokes equations with vacuum and smallness on coefficient-coupled scaling invariant quantity

We investigate the Cauchy problem of three-dimensional compressible Navier-Stokes equations with far-field vacuum. Based on delicate energy estimates and structures of the systems under consideration, we show the global well-posedness and decay rates of strong solutions provided that some coefficient-coupled scaling invariant initial quantity is suitably small. In particular, our smallness conditions are independent of any initial data and known parameters in the systems. Moreover, there is no need to require the compatibility conditions on the initial data. Our results improve previous works.