WIAS Preprint No. 2869, (2021)

Maximal mixed parabolic-hyperbolic regularity for the full equations of multicomponent fluid dynamics


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

2020 Mathematics Subject Classification

  • 35M33 76N10 35Q35 35Q79 35D35 80A17 80A32


  • Multicomponent fluids, continuum thermodynamics, PDE system of mixed type, local-in-time well-posedness, maximal regularity




We consider a Navier--Stokes--Fick--Onsager--Fourier system of PDEs describing mass, energy and momentum balance in a Newtonian fluid with composite molecular structure. For the resulting parabolic-hyperbolic system, we introduce the notion of optimal regularity of mixed type, and we prove the short-time existence of strong solutions for a typical initial boundary-value-problem. By means of a partial maximum principle, we moreover show that such a solution cannot degenerate in finite time due to blow-up or vanishing of the temperature or the partial mass densities. This second result is however only valid under certain growth conditions on the phenomenological coefficients. In order to obtain some illustration of the theory, we set up a special constitutive model for volume-additive mixtures.

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