Differential and Integral Equations

Derivation of hydrodynamic limit from Knudsen gas model

Christian Dogbe

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Abstract

We prove that the solutions of the kinetic equation modelling the reflection of particles according to a reversible law and considered on the $n$-torus converge to the diffusion equation when the main free path goes to zero. This extends the work of Bardos, Golse and Colonna [2] to the case of any $n$-dimensional torus ergodic automorphism.

Article information

Source
Differential Integral Equations, Volume 19, Number 6 (2006), 681-696.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356050358

Mathematical Reviews number (MathSciNet)
MR2234719

Zentralblatt MATH identifier
1212.82006

Subjects
Primary: 82C40: Kinetic theory of gases
Secondary: 28D05: Measure-preserving transformations 35B25: Singular perturbations 35F25: Initial value problems for nonlinear first-order equations 76A02: Foundations of fluid mechanics 76P05: Rarefied gas flows, Boltzmann equation [See also 82B40, 82C40, 82D05]

Citation

Dogbe, Christian. Derivation of hydrodynamic limit from Knudsen gas model. Differential Integral Equations 19 (2006), no. 6, 681--696. https://projecteuclid.org/euclid.die/1356050358


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