The incompressible Navier-Stokes-Fourier limit from Boltzmann-Fermi-Dirac equation

We study Boltzmann-Fermi-Dirac equation when quantum effects are taken into account in dilute gas dynamics. By employing new estimates on trilinear terms in collision integral, we prove the global existence of the classical solution to Boltzmann-Fermi-Dirac equation near equilibrium. Furthermore, the limit from Boltzmann-Fermi-Dirac equation to incompressible Navier-Stokes-Fourier equations is justified rigorously, which was formally derived in the thesis of Zakrevskiy [48]. (c) 2021 Elsevier Inc. All rights reserved.

Automated summary

We investigated the Boltzmann-Fermi-Dirac equation in dilute gas dynamics considering quantum effects, and proved the global existence of classical solution near equilibrium by new estimates on trilinear terms in the collision integral. Additionally, we rigorously justified the limit from the Boltzmann-Fermi-Dirac equation to the incompressible Navier-Stokes-Fourier equations, which was formally derived by Zakrevskiy.