Abstract
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.
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