Global Well-Posedness to the 3D Cauchy Problem of Nonhomogeneous Heat Conducting Navier-Stokes Equations with Vacuum and Large Oscillations

We study global well-posedness of strong solutions to the Cauchy problem of nonhomogeneous heat conducting Navier-Stokes equations with vacuum on the whole space R-3. We derive the global existence and uniqueness of strong solutions provided that parallel to rho(0)parallel to L-infinity parallel to root rho(0)u(0) parallel to(2)(L2) parallel to del u(0)parallel to(2)(L2) is suitably small, with the smallness depending only on the viscosity coefficient mu of the system under consideration. Moreover, we also obtain the large time decay rates of the solution. In particular, the smallness condition is independent of any norms of the initial data and allows the solution to have large oscillations. Furthermore, there is no need to require compatibility conditions for the initial data via time weighted techniques.