Local existence of strong solution for the Cauchy problem of fully compressible Navier-Stokes equations in two dimensions

ABSTRACT: We  consider  the  Navier-Stokes  equations describing a   viscous compressible and heat-conductive  fluid   in two-dimensional space.     By imposing  a weight function to   initial density  and   constructing  an ad-hoc  cut-off  to  control the  quadratic nonlinearity  in temperature  equation,   We prove the local in time existence of strong solutions for the Cauchy problem.  There is no  restriction on the size of the initial data, and the    vacuum state    at infinity  or the compactly supported density  is  permitted.