Compressible Navier–Stokes approximation to the Boltzmann equation

Shuangqian Liu; Tong Yang; Huijiang Zhao

doi:10.1016/j.jde.2014.02.020

Author(s)

Related Research Unit(s)

Department of Mathematics

Detail(s)

Original language	English
Pages (from-to)	3770-3816
Journal / Publication	Journal of Differential Equations
Volume	256
Issue number	11
Online published	14 Mar 2014
Publication status	Published - 1 Jun 2014

Link(s)

DOI	DOI https://doi.org/10.1016/j.jde.2014.02.020 Final Published version
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Link to Scopus	https://www.scopus.com/record/display.uri?eid=2-s2.0-84897385049&origin=recordpage
Permanent Link	https://scholars.cityu.edu.hk/en/publications/publication(0e1c8689-5aa6-4d8c-86c8-8da3c01c4914).html

Abstract

Even though the system of the compressible Navier-Stokes equations is not a limiting system of the Boltzmann equation when the Knudsen number tends to zero, it is the second order approximation by applying the Chapman-Enskog expansion. The purpose of this paper is to justify this approximation rigorously in mathematics. That is, if the difference between the initial data for the compressible Navier-Stokes equations and the Boltzmann equation is of the second order of the Knudsen number, so is the difference between two solutions for all time. The analysis is based on a refined energy method for a fluid-type system using the techniques for the system of viscous conservation laws. © 2014 Elsevier Inc.

Citation Format(s)

[ RIS ] [ BibTeX ]

Compressible Navier–Stokes approximation to the Boltzmann equation. / Liu, Shuangqian ; Yang, Tong; Zhao, Huijiang.

In: Journal of Differential Equations, Vol. 256, No. 11, 01.06.2014, p. 3770-3816.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review

Liu, S , Yang, T & Zhao, H 2014, 'Compressible Navier–Stokes approximation to the Boltzmann equation', Journal of Differential Equations, vol. 256, no. 11, pp. 3770-3816. https://doi.org/10.1016/j.jde.2014.02.020

Liu, S., Yang, T., & Zhao, H. (2014). Compressible Navier–Stokes approximation to the Boltzmann equation. Journal of Differential Equations, 256(11), 3770-3816. https://doi.org/10.1016/j.jde.2014.02.020

Liu S , Yang T, Zhao H. Compressible Navier–Stokes approximation to the Boltzmann equation. Journal of Differential Equations. 2014 Jun 1;256(11):3770-3816. Epub 2014 Mar 14. doi: 10.1016/j.jde.2014.02.020

Liu, Shuangqian ; Yang, Tong ; Zhao, Huijiang. / Compressible Navier–Stokes approximation to the Boltzmann equation. In: Journal of Differential Equations. 2014 ; Vol. 256, No. 11. pp. 3770-3816.