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arXiv · 1912.01677

BGK model of the multi-species Uehling-Uhlenbeck equation

Gi-Chan Bae·Christian Klingenberg·Marlies Pirner·Seok-Bae Yun
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Abstract

We propose a BGK model of the quantum Boltzmann equation for gas mixtures. We also provide a sufficient condition that guarantees the existence of equilibrium coefficients so that the model shares the same conservation laws and $H$-theorem with the quantum Boltzmann equation. Unlike the classical BGK for gas mixtures, the equilibrium coefficinets of the local equilibiriums for quantum multi-species gases are defined through highly nonlinear relations that are not explicitly solvable. We verify in a unified way that such nonlinear relations uniquely determine the equilibrium coefficients under the condition, leading to the well-definedness of our model.

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Gi-Chan Bae, Christian Klingenberg, Marlies Pirner, Seok-Bae Yun. 2019-12-03. BGK model of the multi-species Uehling-Uhlenbeck equation. https://arxiv.org/abs/1912.01677

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