Electron. J. Diff. Eqns., Vol. 2004(2004), No. 104, pp. 118.
From discrete Boltzmann equation to compressible
linearized Euler equations
Abdelghani Bellouquid
Abstract:
This paper concerns the asymptotic analysis of the linearized
Euler limit for a general discrete velocity model of the
Boltzmann equation. This is done for any dimension of the physical
space, for densities which remain in a suitable small
neighbourhood of global Maxwellians. Providing that the initial
fluctuations are smooth, the scaled solutions of discrete
Boltzmann equation are shown to have fluctuations that locally
in time converge weakly to a limit governed by a solution
of linearized Euler equations. The weak limit becomes strong
when the initial fluctuations converge to appropriate initial data.
As applications, the twodimensional 8velocity model and the
onedimensional Broadwell model are analyzed in detail.
Submitted February 5, 2004. Published September 8, 2004.
Math Subject Classifications: 58J05, 53C21.
Key Words: Discrete Boltzmann equation; kinetic theory;
asymptotic theory; compressible Euler; Broadwell model.
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Abdelghani Bellouquid
Department of Mathematics, Politecnico of Torino
Corso Duca degli Abruzzi
24, 10129, Torino, Italy
email: bellouq@calvino.polito.it 
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