Title: A new characterization of the dissipation structure and the relaxation limit for the compressible Euler-Maxwell system Show Chinese title

Title: 关于可压缩欧拉-麦克斯韦系统耗散结构和松弛极限的一个新的刻画

Abstract: We investigate the three-dimensional compressible Euler-Maxwell system, a model for simulating the transport of electrons interacting with propagating electromagnetic waves in semiconductor devices. First, we show the global well-posedness of classical solutions being a sharp small perturbation of constant equilibrium in a critical regularity setting, uniformly with respect to the relaxation parameter $\varepsilon>0$. Then, for all times $t>0$, we derive quantitative error estimates at the rate $O(\varepsilon)$ between the rescaled Euler-Maxwell system and the limit drift-diffusion model. To the best of our knowledge, this work provides the first global-in-time strong convergence for the relaxation procedure in the case of ill-prepared data. In order to prove our results, we develop a new characterization of the dissipation structure for the linearized Euler-Maxwell system with respect to the relaxation parameter $\varepsilon$. This is done by partitioning the frequency space into three distinct regimes: low, medium and high frequencies, each associated with a different behaviour of the solution. Then, in each regime, the use of efficient unknowns and Lyapunov functionals based on the hypocoercivity theory leads to uniform a priori estimates. Show Chinese abstract

Abstract: 我们研究了三维可压缩欧拉-麦克斯韦系统，这是一个用于模拟半导体器件中电子与传播的电磁波相互作用传输的模型。 首先，我们在一个临界正则性设定下，证明了经典解的全局适定性，该解是常数平衡状态的一个尖锐的小扰动，并且这种结果对于松弛参数 $\varepsilon>0$ 是一致的。 然后，在所有时间 $t>0$ 上，我们得到了重新标度后的欧拉-麦克斯韦系统与极限漂移扩散模型之间的误差估计，其收敛率为 $O(\varepsilon)$。 据我们所知，这项工作首次提供了在不适备数据情况下松弛过程的时间全局强收敛性。 为了证明我们的结果，我们发展了一种新的线性化欧拉-麦克斯韦系统的耗散结构表征方法，这种方法是关于松弛参数 $\varepsilon$ 进行的。 这是通过将频域空间划分为三个不同的区域来实现的：低频、中频和高频，每个区域都对应于解的不同行为。 然后，在每个区域内，使用基于超 coercivity 理论的有效未知量和李雅普诺夫泛函，可以得到一致的先验估计。