Non-Hydrodynamic Solutions to the linear Density-dependent BGK equation
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866912838542426112 |
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| author | Kogelbauer, Florian |
| author_facet | Kogelbauer, Florian |
| contents | 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 $τ$ for which the dissipation rate of the macroscopic mass density diverges $\sim 1/τ$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_15259 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Non-Hydrodynamic Solutions to the linear Density-dependent BGK equation Kogelbauer, Florian Analysis of PDEs Mathematical Physics 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 $τ$ for which the dissipation rate of the macroscopic mass density diverges $\sim 1/τ$. 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. |
| title | Non-Hydrodynamic Solutions to the linear Density-dependent BGK equation |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2601.15259 |