Fluid dynamic limit to rarefaction wave for the Boltzmann equation

The 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 . In this paper, the convergence rate of Xin and Zeng (2010) [23] is improved to by different scaling arguments.