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

Thibaut Allemand

doi:10.3934/krm.2009.2.379

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2009, Volume 2, Issue 2: 379-402. Doi: 10.3934/krm.2009.2.379

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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

Received: October 31, 2008

Revised: February 28, 2009

Published: May 2009

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Abstract

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.

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Mathematics Subject Classification: Primary: 76Y05; Secondary: 82C40, 82D50.

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