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 [1] and [2]. 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.

Laurent Desvillettes, F.G. (2019). A Formal Passage From a System of Boltzmann Equations for Mixtures Towards a Vlasov-Euler System of Compressible Fluids. ACTA MATHEMATICAE APPLICATAE SINICA, 35(1), 158-173 [10.1007/s10255-019-0802-1].

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

Valeria Ricci
2019-01-01

Abstract

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 [1] and [2]. 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.
2019
Settore MAT/07 - Fisica Matematica
Laurent Desvillettes, F.G. (2019). A Formal Passage From a System of Boltzmann Equations for Mixtures Towards a Vlasov-Euler System of Compressible Fluids. ACTA MATHEMATICAE APPLICATAE SINICA, 35(1), 158-173 [10.1007/s10255-019-0802-1].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/332880
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