چکیده (انگلیسی):

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 ε 1/5 | ln ε|. In this paper, the convergence rate of Xin and Zeng (2010) [23] is improved to ε 1/3 | ln ε|2 by different scaling arguments.