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A Formal Passage From a System of Boltzmann Equations for Mixtures Towards a Vlasov-Euler System of Compressible Fluids

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Abstract

A formal asymptotics leading from a system of Boltzmann equations for mixtures towards either Vlasov-Navier-Stokes or Vlasov-Stokes equations of incompressible fluids was established by the same authors and Etienne Bernard in: A Derivation of the Vlasov-Navier-Stokes Model for Aerosol Flows from Kinetic Theory Commun. Math. Sci., 15: 1703–1741 (2017) and A Derivation of the Vlasov-Stokes System for Aerosol Flows from the Kinetic Theory of Binary Gas Mixtures. KRM, 11: 43–69 (2018). With the same starting point but with a different scaling, we establish here a formal asymptotics leading to the Vlasov-Euler system of compressible fluids. Explicit formulas for the coupling terms are obtained in two typical situations: for elastic hard spheres on one hand, and for collisions corresponding to the inelastic interaction with a macroscopic dust speck on the other hand.

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References

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Authors and Affiliations

  1. Université Paris Diderot, Sorbonne Paris Cité, Institut de Mathématiques de Jussieu - Paris Rive Gauche, UMR CNRS 7586, CNRS, Sorbonne Universités, UPMC Univ., Paris 06, 75013, Paris, France

    Laurent Desvillettes

  2. CMLS, Ecole polytechnique et CNRS, Université Paris-Saclay, 91128, Palaiseau Cedex, France

    François Golse

  3. Dipartimento di Matematica e Informatica, Università degli Studi di Palermo, Via Archirafi 34, I90123, Palermo, Italy

    Valeria Ricci

Authors
  1. Laurent Desvillettes
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  2. François Golse
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  3. Valeria Ricci
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Corresponding author

Correspondence to Laurent Desvillettes.

Additional information

This paper is dedicated to Professor Philippe G. Ciarlet on the occasion of his 80th birthday.

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Desvillettes, L., Golse, F. & Ricci, V. A Formal Passage From a System of Boltzmann Equations for Mixtures Towards a Vlasov-Euler System of Compressible Fluids. Acta Math. Appl. Sin. Engl. Ser. 35, 158–173 (2019). https://doi.org/10.1007/s10255-019-0802-1

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  • DOI: https://doi.org/10.1007/s10255-019-0802-1

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