# American Institute of Mathematical Sciences

June  2009, 2(2): 379-402. doi: 10.3934/krm.2009.2.379

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

 1 DMA, École Normale Supérieure, 45 rue d'Ulm, 75230 Paris Cedex 05, France

Received  November 2008 Revised  March 2009 Published  May 2009

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.
Citation: Thibaut Allemand. Derivation of a two-fluids model for a Bose gas from a quantum kinetic system. Kinetic and Related Models, 2009, 2 (2) : 379-402. doi: 10.3934/krm.2009.2.379
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