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On a Model for Mixture Flows: Derivation, Dissipation and Stability Properties

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Abstract

We propose a new model describing mixture flows. The non linear system couples heterogeneous Navier–Stokes equations with a constraint on the mean volume velocity of the flow. The PDE system is obtained from a more microscopic viewpoint, involving a Vlasov-like equation describing the disperse phase, through a certain hydrodynamic limit. The model has remarkable dissipation properties, inherited from the structure of the fluid-kinetic description. Based on these properties, together with additional estimates that can be obtained in the one-dimension framework, we establish the stability of weak solutions.

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Authors and Affiliations

  1. Project-Team COFFEE, INRIA Sophia Antipolis Méditerranée & Labo. J. A. Dieudonné UMR 7351, CNRS-Université Nice Sophia Antipolis, Parc Valrose, 06108, Nice Cedex, France

    Thierry Goudon

  2. Department of Mathematics, University of Texas at Austin, Austin, TX, 78712, USA

    Alexis Vasseur

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  1. Thierry Goudon
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  2. Alexis Vasseur
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Correspondence to Thierry Goudon.

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Communicated by L. Saint-Reymond

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Goudon, T., Vasseur, A. On a Model for Mixture Flows: Derivation, Dissipation and Stability Properties. Arch Rational Mech Anal 220, 1–35 (2016). https://doi.org/10.1007/s00205-015-0925-3

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