Stationary Solutions to the Boltzmann Equation in the Hydrodynamic Limit

被引：2
|
作者：
Esposito R. [1 ]
Guo Y. [2 ]
Kim C. [3 ]
Marra R. [4 ]
机构：
[1] International Research Center M&MOCS, Univ. dell’Aquila, Cisterna di Latina, 04012, LT
[2] Division of Applied Mathematics, Brown University, Providence, 02812, RI
[3] Department of Mathematics, University of Wisconsin, Madison, 53706-1325, WI
[4] Dipartimento di Fisica and Unità INFN, Università di Roma Tor Vergata, Rome
来源：
Annals of PDE | 2018年 / 4卷 / 1期
基金：
中国国家自然科学基金; 美国国家科学基金会;
关键词：
Boltzmann equation; Hydrodynamic limit; Navier–Stokes equation;
D O I：
10.1007/s40818-017-0037-5
中图分类号：
学科分类号：
摘要：
Despite its conceptual and practical importance, a rigorous derivation of the steady incompressible Navier–Stokes–Fourier system from the Boltzmann theory has been an outstanding open problem for general domains in 3D. We settle this open question in the affirmative, in the presence of a small external field and a small boundary temperature variation for the diffuse boundary condition. We employ a recent quantitative L2–L∞ approach with new L6 estimates for the hydrodynamic part Pf of the distribution function. Our results also imply the validity of Fourier law in the hydrodynamical limit, and our method leads to an asymptotical stability of steady Boltzmann solutions as well as the derivation of the unsteady Navier–Stokes–Fourier system. © 2017, Springer International Publishing AG.
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