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 - 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

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

Domains: Mathematics [math]; Analysis of PDEs [math.AP]; Physics [physics]; Mechanics [physics]; Fluid mechanics [physics.class-ph]

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 , 2018, 11 (1), pp.43-69. ⟨10.3934/krm.2018003⟩. ⟨hal-01717822⟩