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

This issue Previous Article Orbit counting in polarized dynamical systems Next Article Families of vector fields with many numerical invariants

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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