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This paper investigates the Cauchy problem of two-dimensional fullcompressible Navier-Stokes system with density and temperature vanishing atinfinity. For the strong solutions, some a priori weighted $L^2(R^2)$-norm ofthe gradient of velocity is obtained by the techniques of $A_p$ weights andcancellation of singularity. Based on this key weighted estimate and some basicweighted analysis of velocity and temperature, we establish the local existenceand uniqueness of strong solutions with initial vacuum by means of a two-levelapproximation scheme. Meanwhile, for $q_1$ and $q_2$ as in (1.8), the$L^\infty_tL^{q_1}_x$-norm of velocity and the $L^2_tL^{q_2}_x$-norm oftemperature are derived originally. Moreover, we obtain a blowup criterion onlyin terms of the temporal integral of the maximum norm of divergence ofvelocity, which is independent of the temperature.

On Existence and Blowup Criterion of Strong Solutions to Cauchy Problem of 2D Full Compressible Navier-Stokes System with Vacuum