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PreprintCC BY 4.0HAL

Hydrodynamic Limit of a Viscous BGK Model of the Boltzmann Equation

  • Gabriella Puppo
  • Thomas Rey
  • Tommaso Tenna
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Abstract

In this paper, we investigate a viscous regularization for the BGK model of the Boltzmann equation and its hydrodynamic limit. First, we establish rigorous convergence toward the viscous Euler equations, by exploiting bounds derived from spatial Fisher information. We then analyze the formal derivation of the Euler equations with an entropy inequality for both single-and multi-species case, comparing our results against symmetric hyperbolic thermodynamically compatible theory.

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Cite

BibTeXRIS
BibTeX
@misc{puppo2026hydrodynamic,
  title = {{Hydrodynamic Limit of a Viscous BGK Model of the Boltzmann Equation}},
  author = {Gabriella Puppo and Thomas Rey and Tommaso Tenna},
  howpublished = {HAL},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.39283},
  eprint = {2609.39283},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05769994v1},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Hydrodynamic Limit of a Viscous BGK Model of the Boltzmann Equation
AU  - Gabriella Puppo
AU  - Thomas Rey
AU  - Tommaso Tenna
PY  - 2026
DA  - 2026/09/29
PB  - HAL
DO  - 10.48550/arxiv.2609.39283
UR  - https://hal.science/hal-05769994v1
AB  - In this paper, we investigate a viscous regularization for the BGK model of the Boltzmann equation and its hydrodynamic limit. First, we establish rigorous convergence toward the viscous Euler equations, by exploiting bounds derived from spatial Fisher information. We then analyze the formal derivation of the Euler equations with an entropy inequality for both single-and multi-species case, comparing our results against symmetric hyperbolic thermodynamically compatible theory.
ER  -