Bellouquid, Abdelghani From discrete Boltzmann equation to compressible linearized Euler equations. (English) Zbl 1070.35026 Electron. J. Differ. Equ. 2004, Paper No. 104, 18 p. (2004). 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. Cited in 1 Document 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 Keywords:kinetic theory; asymptotic theory; compressible Euler equation; Broadwell model PDFBibTeX XMLCite \textit{A. Bellouquid}, Electron. J. Differ. Equ. 2004, Paper No. 104, 18 p. (2004; Zbl 1070.35026) Full Text: EuDML EMIS