The relaxation limit of bipolar fluid models

TL;DR

This paper rigorously proves the convergence of bipolar fluid models from a complex Euler-Poisson system to a simpler drift-diffusion system under high-friction conditions, using a relative energy method.

Contribution

It introduces a relative energy framework to establish the relaxation limit from bipolar Euler-Poisson to bipolar drift-diffusion models.

Findings

Convergence of weak solutions to strong solutions in the high-friction regime.

Development of a relative energy identity for bipolar fluid systems.

Validation of the relaxation limit under smooth solution assumptions.

Abstract

This work establishes the relaxation limit from the bipolar Euler-Poisson system to the bipolar drift-diffusion system, for data so that the latter has a smooth solution. A relative energy identity is developed for the bipolar fluid system and is used to show that a dissipative weak solution of the bipolar Euler-Poisson system converges in the high-friction regime to a strong and bounded away from vacuum solution of the bipolar drift-diffusion system.