Bobylev A V
Keldysh Institute for Applied Mathematics, RAS, Moscow, 125047, Russian Federation
Philos Trans A Math Phys Eng Sci. 2018 Apr 28;376(2118). doi: 10.1098/rsta.2017.0227.
We consider in this paper the problem of derivation and regularization of higher (in Knudsen number) equations of hydrodynamics. The author's approach based on successive changes of hydrodynamic variables is presented in more detail for the Burnett level. The complete theory is briefly discussed for the linearized Boltzmann equation. It is shown that the best results in this case can be obtained by using the 'diagonal' equations of hydrodynamics. Rigorous estimates of accuracy of the Navier-Stokes and Burnett approximations are also presented.This article is part of the theme issue 'Hilbert's sixth problem'.
在本文中，我们考虑了更高阶（以克努森数衡量）流体动力学方程的推导和正则化问题。对于伯内特阶次，基于流体动力学变量的连续变化，对作者的方法进行了更详细的阐述。针对线性化玻尔兹曼方程，简要讨论了完整理论。结果表明，在这种情况下，通过使用流体动力学的“对角”方程可获得最佳结果。同时还给出了纳维 - 斯托克斯近似和伯内特近似精度的严格估计。本文是“希尔伯特第六问题”主题专刊的一部分。
