Fluid dynamic limit to rarefaction wave for the Boltzmann equation

AbstractThe hydrodynamic limit for the Boltzmann equation to the compressible Euler equation as Knudsen number ε vanishes is a difficult and challenging problem in the mathematics. When the corresponding compressible Euler equation has a single rarefaction wave, Xin and Zeng (2010) [23] recently verified the hydrodynamic limit as ε tends to zero with a convergence rate ε15|lnε|. In this paper, the convergence rate of Xin and Zeng (2010) [23] is improved to ε13|lnε|2 by different scaling arguments