On the asymptotic analysis of kinetic models towards the compressible Euler and acoustic equations

This paper deals with the analysis of the asymptotic limit for models of the mathematical kinetic theory to the nonlinearized compressible Euler equations or to the acoustic equations when the Knudsen number epsilon tends to zero. Existence and uniqueness theorems are proven for analytic initial fluctuations on the time interval independent of the small parameter epsilon. As epsilon tends to zero, the solution of kinetics models converges strongly to the Maxwellian whose fluid-dynamics parameters solve the Euler and the acoustic systems. The general results are specifically applied to the analysis of the Boltzmann and BGK equations.