Combined relaxation and non-relativistic limit of non-isentropic Euler–Maxwell equations

Abstract

This paper is devoted to study the combined relaxation and non-relativistic limit of non-isentropic Euler-Maxwell equations with relaxation for semiconductors and plasmas. We prove that, as the relaxation time tends to zero and the light speed tends to infinite, periodic initial-value problem of a certain scaled non-isentropic Euler-Maxwell equations has unique smooth solution existing in the time interval where the corresponding classical driftdiffusion model has smooth solutions. It is shown that the relaxation regime plays a decisive role in the combined limit. Furthermore, the corresponding convergence rate is obtained.

Global relaxation and nonrelativistic limit of nonisentropic Euler‐Maxwell systems

“…In the recent years, there have been a lot of literatures on the small physical parameters limit of Euler‐Maxwell systems. For the local‐in‐time uniform convergence, one can refer to the previous studies for both isentropic and nonisentropic Euler‐Maxwell systems. While for the global‐in‐time uniform convergence, there are only a few results on the small parameters limit for Euler‐Maxwell systems.…”

A regularity criterion for the compressible hydrodynamic‐Maxwell system

“…Guo and Tahvildar-Zadeh [5] showed a regularity criterion for spherically symmetric case of the system (1.2)-(1.6). The diffusive relaxation limit and non-relativistic limit to the system (1.1) were studied in [14][15][16].…”