A DERIVATION OF THE VLASOV-STOKES SYSTEM FOR AEROSOL FLOWS FROM THE KINETIC THEORY OF BINARY GAS MIXTURES

Etienne Bernard 1 Laurent Desvillettes 2 François Golse 3 Valeria Ricci 4
1 LAREG/IGN - LAboratoire de REcherche en Géodésie [Paris]
2 IMJ - Institut de Mathématiques de Jussieu
3 CMLS - Centre de Mathématiques Laurent Schwartz
4 Dipartimento di Matematica e Informatica
Abstract : In this short 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, arXiv:1608.00422[math.AP]] where the evolution of the gas is governed by the Navier-Stokes equation.
Keywords : Boltzmann equation hydrodynamic limit aerosols sprays gas mixture. Vlasov-Stokes system
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Submitted on : Monday, February 26, 2018 - 6:31:48 PM
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Etienne Bernard, Laurent Desvillettes, François Golse, Valeria Ricci. A DERIVATION OF THE VLASOV-STOKES SYSTEM FOR AEROSOL FLOWS FROM THE KINETIC THEORY OF BINARY GAS MIXTURES. Kinetic and Related Models , AIMS, 2018, 11 (1), pp.43-69. ⟨10.3934/krm.2018003⟩. ⟨hal-01717822⟩

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