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From discrete Boltzmann equation to compressible linearized Euler equations. (English) Zbl 1070.35026

Summary: 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. Provided that the initial fluctuations are smooth, the scaled solutions of discrete Boltzmann equation are shown to have fluctuations that converge locally in time weakly to a limit governed by a solution of linearized Euler equations. The weak limit becomes strong if the initial fluctuations converge to appropriate initial data. As applications, the two-dimensional 8-velocity model and the one-dimensional Broadwell model are analyzed in detail.

MSC:

35Q35 PDEs in connection with fluid mechanics
82C40 Kinetic theory of gases in time-dependent statistical mechanics
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
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