WIAS Preprint No. 2930, (2022)

Incompressible limit for a fluid mixture



Authors

  • Druet, Pierre-Étienne
    ORCID: 0000-0001-5303-0500

2020 Mathematics Subject Classification

  • 76M45 35Q30 76D05 76N06 76T30

Keywords

  • Multicomponent fluid, incompressibility, low Mach-number limit, relative entropy

DOI

10.20347/WIAS.PREPRINT.2930

Abstract

In this paper we discuss the incompressible limit for multicomponent fluids in the isothermal ideal case. Both a direct limit-passage in the equation of state and the low Mach-number limit in rescaled PDEs are investigated. Using the relative energy inequality, we obtain convergence results for the densities and the velocity-field under the condition that the incompressible model possesses a sufficiently smooth solution, which is granted at least for a short time. Moreover, in comparison to single-component flows, uniform estimates and the convergence of the pressure are needed in the multicomponent case because the incompressible velocity field is not divergence-free. We show that certain constellations of the mobility tensor allow to control gradients of the entropic variables and yield the convergence of the pressure in L1.

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