Approximations of Euler-Maxwell systems by drift-diffusion equations through zero-relaxation limits near non-constant equilibrium
Abstract
Due to extreme difficulties in numerical simulations of Euler-Maxwell equations, which are caused by the highly complicated structures of the equations, this paper concerns the simplification of Euler-Maxwell system through the zero-relaxation limit towards the drift-diffusion equations with non-constant doping functions. We carry out the global-in-time convergence analysis by establishing uniform estimates of solutions near non-constant equilibrium regarding the relaxation parameter and passing to the limit by using classical compactness arguments. Furthermore, stream function methods are carefully generalized to the non-constant equilibrium case, with which as well as the anti-symmetric structure of the error system and an induction argument, we establish global-in-time error estimates between smooth solutions to the Euler-Maxwell system and those to drift-diffusion system, which are bounded by some power of relaxation parameter.
Cite
@article{arxiv.2312.07314,
title = {Approximations of Euler-Maxwell systems by drift-diffusion equations through zero-relaxation limits near non-constant equilibrium},
author = {Rui Jin and Yachun Li and Liang Zhao},
journal= {arXiv preprint arXiv:2312.07314},
year = {2023}
}