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

被引：15

作者：

Bernard, Etienne ^{[1
]}

Desvillettes, Laurent ^{[2
]}

Golse, Francois ^{[3
,4
]}

Ricci, Valeria ^{[5
]}

机构：

[1] Univ Paris Diderot, IGN LAREG, Batiment Lamarck A,5 Rue Thomas Mann, F-75205 Paris 13, France

[2] UPMC Univ Paris 06, Univ Paris Diderot, Sorbonne Paris Cite,Sorbonne Univ,CNRS, UMR CNRS 7586,Inst Math Jussieu Paris Rive Gauche, F-75013 Paris, France

[3] Univ Paris Saclay, Ecole Polytech, CMLS, F-91128 Palaiseau, France

[4] Univ Paris Saclay, CNRS, F-91128 Palaiseau, France

[5] Univ Palermo, Dipartimento Matemat & Informat, Via Archirafi 34, I-190123 Palermo, Italy

来源：

关键词：

Vlasov-Stokes system; Boltzmann equation; hydrodynamic limit; aerosols; sprays; gas mixture; RAREFIED-GAS; HYDRODYNAMIC LIMIT; PARTICLES REGIME; WEAK SOLUTIONS; UNIFORM-FLOW; EQUATIONS; FLUID; TRANSPORT; SPHERE; MODEL;

D O I：

10.3934/krm.2018003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：43 / 69

页数：27

共 37 条

[11] Global well-posedness and large-time behavior for the inhomogeneous Vlasov-Navier-Stokes equations [J].