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First of all, we get the global existence of classical and strong solutionsof the full compressible Navier-Stokes equations in three space dimensions withinitial data which is large and spherically or cylindrically symmetric. Theappearance of vacuum is allowed. In particular, if the initial data isspherically symmetric, the space dimension can be taken not less than two. Theanalysis is based on some delicate {\it a priori} estimates globally in timewhich depend on the assumption $\kappa=O(1+\theta^q)$ where $q>r$ ($r$ can bezero), which relaxes the condition $q\ge2+2r$ in [14,29,42]. This could beviewed as an extensive work of [18] where the equations hold in the sense ofdistributions in the set where the density is positive with initial data whichis large, discontinuous, and spherically or cylindrically symmetric in threespace dimension. Finally, with the assumptions that vacuum may appear and thatthe solutions are not necessarily symmetric, we establish a blow-up criterionin terms of $\|\rho\|_{L^\infty_tL_x^\infty}$ and$\|\rho\theta\|_{L^4_tL^(12/5)_x}$ for strong solutions.

Global symmetric classical and strong solutions of the full compressible Navier-Stokes equations with vacuum and large initial data