In this paper, we investigate the global well-posedness and optimal time-decay of classical solutions for the 3-D full compressible Navier-Stokes system, which is given by the motion of the compressible viscous and heat-conductive gases. First of all, we study the global well-posedness of the Cauchy problem to the system when the initial data is small enough. Secondly, we show the optimal decay rates of the higher-order spatial derivatives of the Ḣ^-s (0 s<32) negative Sobolev norms. Finally, under the assumption that the initial data is bounded in L^1-norm, we establish the upper and lower bounds of the optimal decay rates for the classical solutions.
Huo et al. (Tue,) studied this question.