Existence and conservation laws for the Boltzmann-Fermi-Dirac equation in a general domain [Existence et lois de conservation pour l'équation de Boltzmann-Fermi-Dirac dans un domaine quelconque]

摘要

We prove an existence theorem for the Boltzmann-Fermi-Dirac equation for integrable collision kernels in possibly bounded domains with specular reflection at the boundaries, using the characteristic lines of the free transport. We then obtain that the solution satisfies the local conservations of mass, momentum and kinetic energy thanks to a dispersion technique.