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

2026/07/29 by Timothée Crin-Barat, Belkacem Said-Houari
Mathematics · #math.AP

paper · pdf

33 pages

arxiv created 2026/07/29 · arxiv updated 2026/07/30

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 \citeDuan_Klem_Zhu₂010,Duan_Ruan_Zhu₂012. In addition, we establish optimal time-decay estimates for solutions with initial data in the critical Besov space B_2,∞^-d/2(ℝ^d), thus extending previous results obtained under the stronger assumption L¹(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 B^-d/2-1_2,∞(\mathbb R^d).

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