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arXiv · 2305.01297

Properties of Non-Equilibrium Steady States for the non-linear BGK equation on the torus

Josephine Evans·Angeliki Menegaki
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Abstract

We study the non-linear BGK model in 1d coupled to a spatially varying thermostat. We show existence, local uniqueness and linear stability of a steady state when the linear coupling term is large compared to the non-linear self interaction term. This model possesses a non-explicit spatially dependent non-equilibrium steady state. We are able to successfully use hypocoercivity theory in this case to prove that the linearised operator around this steady state posesses a spectral gap.

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Josephine Evans, Angeliki Menegaki. 2023-05-02. Properties of Non-Equilibrium Steady States for the non-linear BGK equation on the torus. https://arxiv.org/abs/2305.01297

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