Existence and conservation laws for the Boltzmann-Fermi equation in a general domain

Thibaut Allemand (1)

1 DMA - Département de Mathématiques et Applications - ENS Paris

We give an existence theorem for the Boltzmann-Fermi-Dirac equation for integrable collision cross-sections in general domains with specular reflection at the boundaries, using the characteristic lines of the free transport. We then show that the solution satisfies the local conservations of mass, momentum and kinetic energy, which is the main novelty compared to previous results. This is done thanks to a dispersion technique.

Mots clés: Boltzmann equation; Fermi-Dirac; conservation laws

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

Thibaut Allemand. Existence and conservation laws for the Boltzmann-Fermi equation in a general domain. 2009. ⟨hal-00425055v1⟩