A derivation of the Vlasov-Stokes system for aerosol flows from the kinetic theory of binary gas mixtures

Etienne Bernard; Laurent Desvillettes; François Golse; Valeria Ricci

doi:10.3934/krm.2018003

Article Contents

2018, Volume 11, Issue 2: 1-27. Doi: 10.3934/krm.2018003

This issue Previous Article A non-relativistic model of plasma physics containing a radiation reaction term Next Article Asymptotic behavior of the compressible non-isentropic Navier-Stokes-Maxwell system in $\mathbb{R}^3$

A derivation of the Vlasov-Stokes system for aerosol flows from the kinetic theory of binary gas mixtures

1.
IGN-LAREG, Université Paris Diderot, Bâtiment Lamarck A, 5 rue Thomas Mann, Case courrier 7071,75205 Paris Cedex 13, France
2.
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
3.
CMLS, Ecole polytechnique et CNRS, Université Paris-Saclay, 91128 Palaiseau Cedex, France
4.
Dipartimento di Matematica e Informatica, Universitá degli Studi di Palermo, Via Archirafi 34, I90123 Palermo, Italy

Received: October 2016

Revised: March 2017

Published: April 2018

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Abstract

In this paper, we formally derive the thin spray equation for a steady Stokes gas (i.e. the equation consists in a coupling between a kinetic — Vlasov type — equation for the dispersed phase and a — steady — Stokes equation for the gas). Our starting point is a system of Boltzmann equations for a binary gas mixture. The derivation follows the procedure already outlined in [Bernard, Desvillettes, Golse, Ricci, Commun.Math.Sci., 15 (2017), 1703–1741] where the evolution of the gas is governed by the Navier-Stokes equation.

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Mathematics Subject Classification: Primary:35Q20, 35B25;Secondary:82C40, 76T15, 76D07.

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