WIAS Preprint No. 2720, (2020)

Well-posedness analysis of multicomponent incompressible flow models



Authors

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

2010 Mathematics Subject Classification

  • 35M33 35Q30 76N10 35D35 35B65 35B35 35K57 35Q35 35Q79 76R50 80A17 80A32 92E20

Keywords

  • Multicomponent flow, complex fluid, fluid mixture, incompressible fluid, low Mach-number, strong solutions

DOI

10.20347/WIAS.PREPRINT.2720

Abstract

In this paper, we extend our study of mass transport in multicomponent isothermal fluids to the incompressible case. For a mixture, incompressibility is defined as the independence of average volume on pressure, and a weighted sum of the partial mass densities of the species stays constant. In this type of models, non solenoidal effects affect the velocity field in the Navier--Stokes equations and, due to different specific volumes of the species, the pressure remains connected to the densities by algebraic formula. By means of a change of variables in the transport problem, we equivalently reformulate the PDE system as to eliminate positivity and incompressibility constraints affecting the density, and prove two type of results: the local-in-time well-posedness in classes of strong solutions, and the global-in-time existence of solutions for initial data sufficiently close to a smooth equilibrium solution.

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