A consistent kinetic model for a two-component mixture with an application to plasma

Christian Klingenberg; Marlies Pirner; Gabriella Puppo

doi:10.3934/krm.2017017

Article Contents

2017, Volume 10, Issue 2: 445-465. Doi: 10.3934/krm.2017017

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A consistent kinetic model for a two-component mixture with an application to plasma

1.
Dept. of Mathematics at Würzburg University, Emil Fischer Str. 40, Würzburg, 97074, Germany
2.
Università degli Studi dell'Insubria, Via Valleggio, Como, 22100, Italy

Received: December 31, 2015

Revised: May 31, 2016

Published: May 2017

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Abstract

We consider a non reactive multi component gas mixture.We propose a class of models, which can be easily generalized to multiple species. The two species mixture is modelled by a system of kinetic BGK equations featuring two interaction terms to account for momentum and energy transfer between the species. We prove consistency of our model: conservation properties, positivity of the solutions for the space homogeneous case, positivity of all temperatures, H-theorem and convergence to a global equilibrium in the space homogeneous case in the form of a global Maxwell distribution. Thus, we are able to derive the usual macroscopic conservation laws. In particular, by considering a mixture composed of ions and electrons, we derive the macroscopic equations of ideal MHD from our model.

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Mathematics Subject Classification: Primary: 82B40, 35Q20; Secondary: 82D10.

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