A new characterization of the dissipation structure and the relaxation limit for the compressible Euler-Maxwell system

Crin-Barat T, Shou LY, Xu J, Peng YJ (2024)


Publication Status: Submitted

Publication Type: Unpublished / Preprint

Future Publication Type: Journal article

Publication year: 2024

URI: https://arxiv.org/abs/2407.00277

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 \textit{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. 

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APA:

Crin-Barat, T., Shou, L.-Y., Xu, J., & Peng, Y.-J. (2024). A new characterization of the dissipation structure and the relaxation limit for the compressible Euler-Maxwell system. (Unpublished, Submitted).

MLA:

Crin-Barat, Timothée, et al. A new characterization of the dissipation structure and the relaxation limit for the compressible Euler-Maxwell system. Unpublished, Submitted. 2024.

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