Global error estimates in zero-relaxation limit of Euler–Poisson system for ion dynamics

Abstract

The zero-relaxation limit of Euler–Poisson systems for ion dynamics in a slow time scale leads to drift-diffusion equations. This fact was justified in previous works. This paper concerns global error estimates between solutions of Euler–Poisson systems and that of drift-diffusion equations. In the proof, we use Sobolev inequalities and employ a multiplier related to the electric potential.

Keywords:

• Zero-relaxation limit
• Euler–Poisson system
• convergence rate

2000 AMS Subject Classifications:

• 35B40
• 35J05
• 35Q35

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Natural Science Foundation of Shandong Province of China [grant number ZR2020MA019].