Work

Properties of non-equilibrium steady states for the non-linear BGK equation on the torus

Year: 2024

Type: article

Abstract: We study the non-linear BGK model in one dimension 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. For the existence and the local uniqueness we utilise a fixed point argument, reducing the study of the non-linear model to the linear BGK model, while for the stability we adapt the L^{2} hypocoercivity theory, yielding existence of a spectral gap for the linearised operator around this non-equilibrium steady state.

Source: Annales de l Institut Henri Poincaré C Analyse Non Linéaire

DOI: 10.4171/aihpc/144

Authors: Josephine Evans, Angeliki Menegaki

Institutions: University of Warwick, Imperial College London

Language: English

Topic: Gas Dynamics and Kinetic Theory

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $700

Funder: Leverhulme Trust