Decay rates to the planar rarefaction waves for a model system of the radiating gas in n dimensions

Abstract

In this paper, we study the asymptotic decay rates to the planar rarefaction waves to the Cauchy problem for a hyperbolic–elliptic coupled system called as a model system of the radiating gas in R n ( n = 3 , 4 , 5 ) if the initial perturbations corresponding to the planar rarefaction waves are sufficiently small in ( H 2 ∩ L 1 ∩ W 2 , 6 ) ( R n ). The analysis is based on the L p -energy method and several special interpolation inequalities.