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 ow equations. We present here a simpler proof than in (D. Bresch, X. Huang, Arch. Ration. Mech. Anal. 2011) to show that the homogeneized system may be reduced to a viscous and compressible multi-component ow system (with one velocity eld) 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-uid system with algebraic closure (pressure equilibrium) in the isothermal case.
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