On the decay estimates of a nonlocal convection-diffusion Hamer system

Abstract

We consider the multi-dimensional Hamer model for radiating gases in its coupled hyperbolic--elliptic formulation. By means of energy estimates, we establish the global well-posedness for small initial data in hybrid Besov spaces with distinct regularity exponents at low and high frequencies. This framework enables us to relax the regularity assumptions required in \cite{Duan_Klem_Zhu_2010,Duan_Ruan_Zhu_2012}. In addition, we establish optimal time-decay estimates for solutions with initial data in the critical Besov space $\dot{B}_{2,\infty}^{-d/2}(\mathbb{R}^d)$, thus extending previous results obtained under the stronger assumption $L^1(\mathbb{R}^d)$. We discuss the optimality of these decay rates and derive improved decay rates under a zero-mass cancellation condition, corresponding to initial data in the larger negative Besov space $\dot B^{-d/2-1}_{2,\infty}(\mathbb R^d)$.