Hydrodynamic limits for the Boltzmann-Fermi-Dirac equation: Acoustic and Stokes-Fourier

We establish the acoustic and Stokes-Fourier hydrodynamic limits for the Boltzmann-Fermi-Dirac (BFD) equation on the torus of dimension 2 or more. For each limit, we consider fluctuations of appropriately scaled solutions of the BFD equation around a constant background Fermi-Dirac distribution. By adapting the weak solution framework developed by Bardos, Golse and Levermore for the classical Boltzmann equation to handle the cubic nonlinearity of the BFD collision operator, we show that these fluctuations converge weakly in time to a unique limit governed by the respective hydrodynamic equation.