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(1981)
Lifshitz: “Physical Kinetics
F. Charles (2009)
Kinetic Modelling and Numerical Simulations using Particle Methods for the Transport of Dust in a Rarefied Gas, 1084
É. Bernard, L. Desvillettes, F. Golse, V. Ricci (2016)
A Derivation of the Vlasov-Navier-Stokes Model for Aerosol Flows from Kinetic TheoryarXiv: Analysis of PDEs
C. Cercignani, R. Street (1970)
Mathematical Methods in Kinetic Theory
É. Bernard, L. Desvillettes, F. Golse, V. Ricci (2016)
A Derivation of the Vlasov-Stokes System for Aerosol Flows from the Kinetic Theory of Binary Gas MixturesarXiv: Analysis of PDEs
L.D. Landau, E.M. Lifshitz (1981)
Course of Theoretical Physics
F. Charles, S. Dellacherie, J. Segré (2012)
KINETIC MODELING OF THE TRANSPORT OF DUST PARTICLES IN A RAREFIED ATMOSPHEREMathematical Models and Methods in Applied Sciences, 22
Frédérique Charles (2009)
Modélisation mathématique et étude numérique d'un aérosol dans un gaz raréfié. Application à la simulation du transport de particules de poussière en cas d'accident de perte de vide dans ITER.
C. Cercignani, R. Aronson (1976)
Theory and application of the Boltzmann equation
F. Charles (2009)
Application à la simulation du transport de particules de poussière en cas d’accident de perte de vide dans ITER
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.
Acta Mathematicae Applicatae Sinica – Springer Journals
Published: Feb 28, 2019
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