The incompressible Euler limit of the Boltzmann equation for a gas of fermions

Thibaut Allemand (1)

1 DMA - Département de Mathématiques et Applications - ENS Paris

We are interested in the hydrodynamic limit of the Boltzmann equation for a gas of fermions in the incompressible Euler regime. We use the relative entropy method as improved by Saint-Raymond. Our result is analogous to what is obtained in the classical case, but the treatment is slightly complicated by the cubic nonlinearity of the collision operator.

Mots clés: quantum Boltzmann equation; fermions; hydrodynamic limit; incompressible Euler; relative entropy

Domaines: Equations aux dérivées partielles [math.AP]

Thibaut Allemand. The incompressible Euler limit of the Boltzmann equation for a gas of fermions. 2010. ⟨hal-00493760v4⟩