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

2021/11/15 by Ning Jiang, Kai Zhou, Jiang, Ning +1 · 2 citations
Engineering · Mathematics · #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Gas Dynamics and Kinetic Theory

paper · pdf · doi:10.48550/arxiv.2111.07784

openalex publication_date 2021/11/15 · openalex created_date 2021/11/22 · openalex updated_date 2026/07/28

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 \citeZakrevskiy 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.

Citations

• The Cauchy problem for quasi-linear symmetric hyperbolic systems
• Symmetric hyperbolic linear differential equations
• Fluid dynamic limits of kinetic equations. I. Formal derivations

Cited by

• The Incompressible Navier-Stokes-Fourier Limits from Boltzmann-Fermi-Dirac Equation for Low Regularity Data
• Incompressible Navier-Stokes-Fourier limit from a nonlinear quantum Fokker-Planck equation

Related

• Acoustic Limit for the Boltzmann equation in Optimal Scaling
• The Incompressible Navier-Stokes-Fourier Limits from Boltzmann-Fermi-Dirac Equation for Low Regularity Data
• The Incompressible Navier-Stokes-Fourier Limit from Boltzmann-Fermi-Dirac Equation
• From the quantum Boltzmann operator to the quantum Landau operator
• The incompressible Euler limit of the Boltzmann equation for a gas of fermions