AI 中文总结
本文研究多维Hamer模型的双曲-椭圆耦合形式，在混合Besov空间中建立小初值全局适定性，放宽了已有正则性假设，还得到临界Besov空间下的最优时间衰减估计，并在零质量条件下推导了改进衰减速率。
AI 中文摘要
我们研究辐射气体的多维Hamer模型，采用其耦合的双曲-椭圆形式表述。通过能量估计方法，我们在低频与高频具有不同正则性指数的混合Besov空间中，建立了小初值下的全局适定性，该框架放宽了Duan_Klem_Zhu_2010、Duan_Ruan_Zhu_2012等文献中要求的正则性假设。此外，我们针对初值属于临界Besov空间$\u200c\dot{B}_{2,\infty}^{-d/2}(\mathbb{R}^d)$的解，建立了最优时间衰减估计，从而推广了此前在更强的$L^1(\mathbb{R}^d)$假设下得到的结果。我们讨论了这些衰减速率的最优性，并在零质量抵消条件下推导了改进的衰减速率，该条件对应初值属于更大的负阶Besov空间$\u200c\dot B^{-d/2-1}_{2,\infty}(\mathbb R^d)$。
英文摘要
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 $\dot B^{-d/2-1}_{2,\infty}(\mathbb R^d)$.
Comments33 pages
