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A Derivation of the Vlasov-Stokes System for Aerosol Flows from the Kinetic Theory of Binary Gas Mixtures

2016

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.

Binary numberKinetic energy01 natural sciencesBoltzmann equationPhysics::Fluid Dynamics35Q20 35B25 82C40 76T15 76D07symbols.namesakeMathematics - Analysis of PDEshydrodynamic limitPhase (matter)FOS: Mathematics[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP][PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph]sprays0101 mathematicsSettore MAT/07 - Fisica MatematicaVlasov-Stokes systemPhysicsNumerical Analysisgas mixture.010102 general mathematicsMSC Primary: 35Q20 35B25; Secondary: 82C40 76T15 76D07.Stokes flowBoltzmann equationAerosol010101 applied mathematicsClassical mechanicsModeling and SimulationBoltzmann constantKinetic theory of gasessymbolsVlasov-Stokes system Boltzmann equation Hydrodynamic limit Aerosols Sprays Gas mixtureaerosolsAnalysis of PDEs (math.AP)
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