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 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.

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. Comptes rendus de l'Académie des sciences. Série I, Mathématique, 2010, 348 (13-14), pp.763-767. ⟨10.1016/j.crma.2010.06.015⟩. ⟨hal-00425055v3⟩