Non-Hydrodynamic Solutions to the linear Density-dependent BGK equation

Florian Kogelbauer

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arXiv · 2601.15259

Non-Hydrodynamic Solutions to the linear Density-dependent BGK equation

Florian Kogelbauer

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Abstract

We prove the existence of non-hydrodynamic solutions to the linear density-dependent BGK equation in $d$ dimensions. Specifically, we show the existence of an initial condition for any Knudsen number $\tau$ for which the dissipation rate of the macroscopic mass density diverges $\sim 1/\tau$. Our results rely on a detailed spectral analysis of the linear BGK operator, an explicit solution formula for the time-dependent problem using a combination of Fourier series with the Laplace transform and subsequent contour integration arguments from complex analysis.

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Florian Kogelbauer. 2026-01-21. Non-Hydrodynamic Solutions to the linear Density-dependent BGK equation. https://arxiv.org/abs/2601.15259

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