Ghost effect for a vapor-vapor mixture

Stéphane Brull

doi:10.3934/krm.2012.5.21

Article Contents

2012, Volume 5, Issue 1: 21-50. Doi: 10.3934/krm.2012.5.21

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Ghost effect for a vapor-vapor mixture

Stéphane Brull^1,

1.
Institut Polytechnique de Bordeaux, 351, cours de la Libération, 33405 TALENCE Cedex

Received: June 2011

Revised: September 2011

Published: March 2012

Abstract / Introduction Related Papers Cited by

Abstract

This paper studies the non linear Boltzmann equation for a two component gas at the small Knudsen number regime. The solution is found from a truncated Hilbert expansion. The first order of the fluid equations shows the ghost effect. The fluid system is solved when the boundary conditions are close enough to each other. Next the boundary conditions for the kinetic system are satisfied by adding for the first and the second order terms of the expansion Knudsen terms. The construction of such boundary layers requires the study of a Milne problem for mixtures. In a last part the rest term of the expansion is rigorously controled by using a new decomposition into a low and a high velocity part.

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Mathematics Subject Classification: 82B40, 76P05.

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