Decay of a model system of radiating gas

This paper concerns the Cauchy problem of a model system to the radiating gas in . Large time behaviors of classical solutions to the Cauchy problem are studied without needing the smallness assumption of initial perturbation in L1-norm. We obtain the optimal HN-norm time-decay rates of the solutions in with 1 ≤ n ≤ 4 by applying the Fourier splitting method introduced by Schonbek (1980) with a slight modification and an energy method. Furthermore, when initial perturbation is bounded in Lp-norm (p ∈ (1,2]), optimal Lp- L2 decay estimates of the derivatives of solutions are shown. Copyright © 2013 John Wiley & Sons, Ltd.