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Note on the derivation of multi-component flow systems


Authors: D. Bresch and M. Hillairet
Journal: Proc. Amer. Math. Soc. 143 (2015), 3429-3443
MSC (2010): Primary 35Q30
DOI: https://doi.org/10.1090/proc/12614
Published electronically: April 21, 2015
MathSciNet review: 3348786
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Abstract: In this note, we justify rigorously the formal method proposed in [M. HILLAIRET, J. Math. Fluid Mech. 2007] to derive viscous and compressible multi-component flow equations. We present here a simpler proof than in [D. BRESCH, X. HUANG, Arch. Ration. Mech. Anal. 2011] to show that the homogenized system may be reduced to a viscous and compressible multi-component flow system (with one velocity-field) getting rid of the no-crossing assumption on the partial densities. We also discuss formally why our multi-component system may be seen as a physically-relevant relaxed system for the well-known bi-fluid system with algebraic closure (pressure equilibrium) in the isothermal case.


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D. Bresch
Affiliation: Laboratoire de Mathématiques, UMR 5127 CNRS, Université de Savoie, 73376 Le Bourget du Lac, France
Email: didier.bresch@univ-savoie.fr

M. Hillairet
Affiliation: Institut de Mathématiques et de Modélisation de Montpellier, Université Montpellier, UMR 5149 CNRS, 34095 Montpellier cedex 5, France
Email: matthieu.hillairet@univ-mont2.fr

DOI: https://doi.org/10.1090/proc/12614
Received by editor(s): August 12, 2013
Published electronically: April 21, 2015
Communicated by: Walter Craig
Article copyright: © Copyright 2015 American Mathematical Society