Note on the derivation of multi-component flow systems

Bresch, D.; Hillairet, M.

doi:10.1090/proc/12614

Note on the derivation of multi-component flow systems
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by D. Bresch and M. Hillairet PDF

Proc. Amer. Math. Soc. 143 (2015), 3429-3443 Request permission

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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