A Formal Passage From a System of Boltzmann Equations for Mixtures Towards a Vlasov-Euler System of Compressible Fluids

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英文篇名：A Formal Passage From a System of Boltzmann Equations for Mixtures Towards a Vlasov-Euler System of Compressible Fluids 作者：Laurent ; DESVILLETTES ; Fran?ois ; GOLSE ; Valeria ; RICCI 英文作者：Laurent DESVILLETTES;Fran?ois GOLSE;Valeria RICCI;Université Paris Diderot, Sorbonne Paris Cité, Institut de Mathématiques de Jussieu-Paris Rive Gauche,UMR CNRS 7586, CNRS, Sorbonne Universités, UPMC Univ;CMLS, Ecole polytechnique et CNRS, Université Paris-Saclay;Dipartimento di Matematica e Informatica, Università degli Studi di Palermo; 英文关键词：Vlasov-Euler system;;Boltzmann equation;;Hydrodynamic limit;;Aerosols;;Sprays;;Gas mixture 中文刊名：YISY 英文刊名：应用数学学报(英文版) 机构：Université Paris Diderot, Sorbonne Paris Cité, Institut de Mathématiques de Jussieu-Paris Rive Gauche,UMR CNRS 7586, CNRS, Sorbonne Universités, UPMC Univ;CMLS, Ecole polytechnique et CNRS, Université Paris-Saclay;Dipartimento di Matematica e Informatica, Università degli Studi di Palermo; 出版日期：2019-01-15 出版单位：Acta Mathematicae Applicatae Sinica 年：2019 期：v.35 基金：funded by the French “ANR blanche” project Kibord:ANR-13-BS01-0004;; by Université Sorbonne Paris Cité,in the framework of the “Investissements d’Avenir”,convention ANR-11-IDEX-0005;; the support by the GNFM(research project 2017:“Analisi rigorosa di sistemi di equazione di tipo reazione–diffusione”) 语种：英文; 页：YISY201901007 页数：16 CN：01 ISSN：11-2041/O1 分类号：162-177

摘要

A formal asymptotics leading from a system of Boltzmann equations for mixtures towards either Vlasov-Navier-Stokes or Vlasov-Stokes equations of incompressible fluids was established by the same authors and Etienne Bernard in: A Derivation of the Vlasov-Navier-Stokes Model for Aerosol Flows from Kinetic Theory Commun. Math. Sci., 15: 1703–1741(2017) and A Derivation of the Vlasov-Stokes System for Aerosol Flows from the Kinetic Theory of Binary Gas Mixtures. KRM, 11: 43–69(2018). With the same starting point but with a different scaling, we establish here a formal asymptotics leading to the Vlasov-Euler system of compressible fluids. Explicit formulas for the coupling terms are obtained in two typical situations: for elastic hard spheres on one hand, and for collisions corresponding to the inelastic interaction with a macroscopic dust speck on the other hand.
        A formal asymptotics leading from a system of Boltzmann equations for mixtures towards either Vlasov-Navier-Stokes or Vlasov-Stokes equations of incompressible fluids was established by the same authors and Etienne Bernard in: A Derivation of the Vlasov-Navier-Stokes Model for Aerosol Flows from Kinetic Theory Commun. Math. Sci., 15: 1703–1741(2017) and A Derivation of the Vlasov-Stokes System for Aerosol Flows from the Kinetic Theory of Binary Gas Mixtures. KRM, 11: 43–69(2018). With the same starting point but with a different scaling, we establish here a formal asymptotics leading to the Vlasov-Euler system of compressible fluids. Explicit formulas for the coupling terms are obtained in two typical situations: for elastic hard spheres on one hand, and for collisions corresponding to the inelastic interaction with a macroscopic dust speck on the other hand.

引文

[1]Bernard,E.,Desvillettes,L.,Golse,F.,Ricci,V.A Derivation of the Vlasov-Navier-Stokes Model for Aerosol Flows from Kinetic Theory.Commun.Math.Sci.,15:1703-1741(2017)
    [2]Bernard,E.,Desvillettes,L.,Golse,F.,Ricci,V.A Derivation of the Vlasov-Stokes System for Aerosol Flows from the Kinetic Theory of Binary Gas Mixtures.KRM,11:43-69(2018)
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