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

Abstract 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] .