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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

Thibaut Allemand 1,

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.
Keywords: hydrodynamic limit, Bose gas, Bose-Einstein condensate..
Mathematics Subject Classification: Primary: 76Y05; Secondary: 82C40, 82D5.
Citation: Thibaut Allemand. Derivation of a two-fluids model for a Bose gas from a quantum kinetic system. Kinetic & Related Models, 2009, 2 (2) : 379-402. doi: 10.3934/krm.2009.2.379
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