The Compressible Euler and Acoustic Limits from quantum Boltzmann Equation with Fermi-Dirac Statistics
Analysis of PDEs
2021-11-16 v1
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.
Keywords
Cite
@article{arxiv.2111.07784,
title = {The Compressible Euler and Acoustic Limits from quantum Boltzmann Equation with Fermi-Dirac Statistics},
author = {Ning Jiang and Kai Zhou},
journal= {arXiv preprint arXiv:2111.07784},
year = {2021}
}
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46 pages