The relaxation limit of bipolar fluid models

Nuno J. Alves; Athanasios E. Tzavaras

doi:10.3934/dcds.2021113

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2022, Volume 42, Issue 1: 211-237. Doi: 10.3934/dcds.2021113

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The relaxation limit of bipolar fluid models

Nuno J. Alves^, and
Athanasios E. Tzavaras

CEMSE Division, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia

^* Corresponding author: Nuno J. Alves
^* Corresponding author: Nuno J. Alves

Received: January 2021

Revised: June 2021

Early access: August 2021

Published: January 2022

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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 models, and it 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.

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Mathematics Subject Classification: Primary: 35Q35, 35Q81; Secondary: 35L65, 35K55, 76W05.

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References

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