Incompressible hydrodynamics as a limit of the boltzmann equation

Franc Lois Golse

doi:10.1080/00411459208203797

Incompressible hydrodynamics as a limit of the boltzmann equation

Franc Lois Golse

Laboratoire de Probabilités et Modèles Aléatoires

Research output: Contribution to journal › Article › peer-review

Abstract

This paper is devoted to proofs of convergence for the incompressible hydrodynamic limits of the Boltzmann equation. It focuses on methods such as entropy control, dissipation control and velocity averaging that allow to treat the case of global weak solutions of the Boltzmann equation (due to DiPema-Lions) converging to global weak solutions of the Navier-Stokes equation (due to Leray). In particular, it shows that the DiPerna-Lions version of the H theorem yields the Leray energy inequality for the Navier-Stokes equation in the limit.

Original language	English
Pages (from-to)	531-555
Number of pages	25
Journal	Transport Theory and Statistical Physics
Volume	21
Issue number	4-6
DOIs	https://doi.org/10.1080/00411459208203797
Publication status	Published - 1 Aug 1992
Externally published	Yes

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10.1080/00411459208203797

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title = "Incompressible hydrodynamics as a limit of the boltzmann equation",

abstract = "This paper is devoted to proofs of convergence for the incompressible hydrodynamic limits of the Boltzmann equation. It focuses on methods such as entropy control, dissipation control and velocity averaging that allow to treat the case of global weak solutions of the Boltzmann equation (due to DiPema-Lions) converging to global weak solutions of the Navier-Stokes equation (due to Leray). In particular, it shows that the DiPerna-Lions version of the H theorem yields the Leray energy inequality for the Navier-Stokes equation in the limit.",

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AB - This paper is devoted to proofs of convergence for the incompressible hydrodynamic limits of the Boltzmann equation. It focuses on methods such as entropy control, dissipation control and velocity averaging that allow to treat the case of global weak solutions of the Boltzmann equation (due to DiPema-Lions) converging to global weak solutions of the Navier-Stokes equation (due to Leray). In particular, it shows that the DiPerna-Lions version of the H theorem yields the Leray energy inequality for the Navier-Stokes equation in the limit.

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ER -

Incompressible hydrodynamics as a limit of the boltzmann equation

Abstract

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