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

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

2009-10-19

arxiv.org/abs/0910.3640v3

Comptes Rendus de l Acad\'emie des Sciences - Series I - Mathematics 348, 13-14 (2010) 763-767

Mathematics

Analysis of PDEs

6 pages

Scientific paper

10.1016/j.crma.2010.06.015

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.

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