3 papers
math.AP2026
Hydrodynamic limits for the Boltzmann-Fermi-Dirac equation: Acoustic and Stokes-Fourier
Paulo Sampaio
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 fluct…
math.AP2025
On the semi-classical limit for the Landau-Fermi-Dirac equation
Paulo Sampaio
We study sequences of solutions to the inhomogeneous Landau-Fermi-Dirac equation with Coulomb potential in which the quantum parameter converges to zero. Our main result establishe…
math.AP2024
Global solutions to the Landau-Fermi-Dirac equation
Paulo Sampaio
We establish a compactness result for solutions of a certain class of hypoelliptic equations. This result allows us to show the existence of global weak solutions to the non-homoge…