Global mild solutions and the semiclassical limit for the Fermi--Dirac BGK model
Abstract
We prove global existence of mild solutions to the spatially inhomogeneous Fermi--Dirac BGK equation for arbitrary-size Pauli-admissible initial data with finite mass and kinetic energy, allowing both vacuum and locally saturated zero-temperature states. The construction relies on a moment-compatible regularization of the local equilibrium that preserves the Pauli bound and uniform moment control while remaining consistent up to the saturation boundary. The solutions satisfy mass, momentum, and energy conservation and, under an additional finite spatial second-moment assumption, an entropy-gap H-theorem on the full Pauli interval. Under uniform moment and entropy bounds, we further prove that, after extraction of a subsequence, quantum mild solutions converge strongly in phase space, uniformly on bounded time intervals, to a mild solution of the classical BGK equation.
Related
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BibTeX
@misc{choi2026global,
title = {{Global mild solutions and the semiclassical limit for the Fermi--Dirac BGK model}},
author = {Young-Pil Choi and Byung-Hoon Hwang and Sihyun Song},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08142},
eprint = {2609.08142},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08142},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Global mild solutions and the semiclassical limit for the Fermi--Dirac BGK model
AU - Young-Pil Choi
AU - Byung-Hoon Hwang
AU - Sihyun Song
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08142
UR - https://arxiv.org/abs/2609.08142
AB - We prove global existence of mild solutions to the spatially inhomogeneous Fermi--Dirac BGK equation for arbitrary-size Pauli-admissible initial data with finite mass and kinetic energy, allowing both vacuum and locally saturated zero-temperature states. The construction relies on a moment-compatible regularization of the local equilibrium that preserves the Pauli bound and uniform moment control while remaining consistent up to the saturation boundary. The solutions satisfy mass, momentum, and energy conservation and, under an additional finite spatial second-moment assumption, an entropy-gap H-theorem on the full Pauli interval. Under uniform moment and entropy bounds, we further prove that, after extraction of a subsequence, quantum mild solutions converge strongly in phase space, uniformly on bounded time intervals, to a mild solution of the classical BGK equation.
ER -