Electronic Journal of Differential Equations,
Vol. 2004(2004), No. 104, pp. 1-18.

Title: From discrete Boltzmann equation to compressible 
       linearized Euler equations

Author: Abdelghani Bellouquid (Politecnico of Torino, Italy)
 
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 two-dimensional 8-velocity model and the 
  one-dimensional 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.