Remarks on global existence and exponential stability of solutions for the viscous radiative and reactive gas with large initial data

In this paper, we study a large time behavior of the global spherically or cylindrically symmetric solutions in H-1 for the compressible viscous radiative and reactive gas in multi-dimension with large initial data. Precisely, if the initial data are spherically symmetric or cylindrically symmetric, the smallness of initial data is not needed. The main concern of the present paper is to investigate the exponential stability of a solution toward the stationary solution as time goes to infinity. We obtain the uniform positive lower and upper bounds of the density by using different methods.