Derivation of a two-fluids model for a Bose gas from a quantum kinetic system

Thibaut Allemand (1)

1 DMA - Département de Mathématiques et Applications - ENS Paris

We formally derive the hydrodynamic limit of a system modelling a bosons gas having a condensed part, made of a quantum kinetic and a Gross-Pitaevskii equation. The limit model, which is a two-fluids Euler system, is approximated by an isentropic system, which is then studied. We find in particular some conditions for the hyperbolicity, and we study the weak solutions. Numerical examples are given at the end.

Mots clés: kinetic equations; Gross-Pitaevskii equation; Bose gas; hydrodynamic limit; hyperbolic system

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

Thibaut Allemand. Derivation of a two-fluids model for a Bose gas from a quantum kinetic system. 2008. ⟨hal-00345084v1⟩