arXiv subjects

Paulo Sampaio

Publications and source records attributed to Paulo Sampaio.

3 recordsLinked to original sources

arXiv2026

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.

math.AP↗

arXiv2026

On the semi-classical limit for the Landau-Fermi-Dirac equation

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 establishes the compactness of these sequences, which allows us to show that, up to a subsequence, these solutions converge to a renormalized solution of the classical Landau equation with a defect measure, as defined by Villani. To do this, we work in the class of solutions that are obtained through approximation procedures. For these solutions, we were able to show compactness in the vanishing quantum parameter limit through a diagonal argument, which combines techniques from the study of Cauchy problems for both the classical Landau and the Landau-Fermi-Dirac equations.

math.AP↗

arXiv2024

Global solutions to the Landau-Fermi-Dirac equation

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-homogeneous Landau-Fermi-Dirac equation with Coulomb potential.

math.AP↗