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arXiv · 2111.07784

The Compressible Euler and Acoustic Limits from quantum Boltzmann Equation with Fermi-Dirac Statistics

Ning Jiang·Kai Zhou
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Abstract

This paper justifies the compressible Euler and acoustic limits from quantum Boltzmann equation with Fermi-Dirac statistics (briefly, BFD) rigorously. This limit was formally derived in Zakrevskiy's thesis \cite{Zakrevskiy} by moment method. We employ the Hilbert approach. The forms of the classical compressible Euler system and the one derived from BFD are different. Our proof is based on the analysis of the nonlinear implicit transformation of these two forms, and a few novel nonlinear estimates.

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Ning Jiang, Kai Zhou. 2021-11-15. The Compressible Euler and Acoustic Limits from quantum Boltzmann Equation with Fermi-Dirac Statistics. https://arxiv.org/abs/2111.07784

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