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. A numerical example is given at the end.

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

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. Kinetic and Related Models , 2009, 2 (2), pp.379 - 402. ⟨10.3934/krm.2009.2.379⟩. ⟨hal-00345084v3⟩