标题： Sobolev空间中可压缩欧拉和欧拉-麦克斯韦系统的松弛极限的全局收敛率 显示英文标题

标题： Global convergence rates in the relaxation limits for the compressible Euler and Euler-Maxwell systems in Sobolev spaces

摘要： 我们研究了部分耗散双曲系统类中的两个松弛问题：带阻尼的可压缩欧拉系统和可压缩欧拉-麦克斯韦系统。 在经典的Sobolev空间中，对于初始数据满足\emph{准备不足的}的情形，我们得到了松弛欧拉系统与$\mathbb{R}^d$中的多孔介质方程（$d\geq1$）之间强解的全局收敛率为$\mathcal{O}(\varepsilon)$。 在准备充分的情况下，我们得到了可压缩欧拉系统解与其一阶渐近逼近之间增强的收敛率，其阶数为$\mathcal{O}(\varepsilon^2)$。 针对欧拉-麦克斯韦系统，我们在$\mathbb{R}^3$中证明了解的全局强收敛性，收敛速率是$\mathcal{O}(\varepsilon)$。 这些结果通过发展一种渐近展开方法实现，结合流函数技术，确保了误差估计在时间上的一致性。 显示英文摘要

摘要： We study two relaxation problems in the class of partially dissipative hyperbolic systems: the compressible Euler system with damping and the compressible Euler-Maxwell system. In classical Sobolev spaces, we derive a global convergence rate of $\mathcal{O}(\varepsilon)$ between strong solutions of the relaxed Euler system and the porous medium equation in $\mathbb{R}^d$ ($d\geq1$) for \emph{ill-prepared} initial data. In a well-prepared setting, we derive an enhanced convergence rate of order $\mathcal{O}(\varepsilon^2)$ between the solutions of the compressible Euler system and their first-order asymptotic approximation. Regarding the Euler-Maxwell system, we prove the global strong convergence of its solutions to the drift-diffusion model in $\mathbb{R}^3$ with a rate of $\mathcal{O}(\varepsilon)$. These results are achieved by developing an asymptotic expansion approach that, combined with stream function techniques, ensures uniform-in-time error estimates.