Journal of Nonlinear Mathematical Physics

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Volume 27, Issue 3, May 2020, Pages 494 - 508

Group analysis of the generalized Burnett equations

Authors
Alexander V. Bobyleva, Sergey V. Meleshkob, *
aKeldysh Institute of Applied Mathematics, Russian Academy of Science, Miusskaya Pl. 4, Moscow, 125047, Russia,alexander.bobylev@kau.se
bSchool of Mathematics, Institute of Science, Suranaree University of Technology, 30000, Thailand,sergey@math.sut.ac.th
*Corresponding author.
Corresponding Author
Sergey V. Meleshko
Received 14 November 2019, Accepted 28 November 2019, Available Online 4 May 2020.
DOI
10.1080/14029251.2020.1757238How to use a DOI?
Keywords
Generalized Burnett equations; Lie group; group classification; conservation law; invariant solutions
Abstract

In this paper group properties of the so-called Generalized Burnett equations are studied. In contrast to the classical Burnett equations these equations are well-posed and therefore can be used in applications. We consider the one-dimensional version of the generalized Burnett equations for Maxwell molecules in both Eulerian and Lagrangian coordinates and perform the complete group analysis of these equations. In particular, this includes finding and analyzing admitted Lie groups. Our classifications of the Lie symmetries of the Navier-Stokes equations of compressible gas and generalized Burnett equations provide a basis for finding invariant solutions of these equations. We also consider representations of all invariant solutions. Some particular classes of invariant solutions are studied in more detail by both analytical and numerical methods.

Copyright
© 2020 The Authors. Published by Atlantis and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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<Previous Article In Issue
Next Article In Issue>
Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
27 - 3
Pages
494 - 508
Publication Date
2020/05/04
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1080/14029251.2020.1757238How to use a DOI?
Copyright
© 2020 The Authors. Published by Atlantis and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

risenwbib
TY  - JOUR
AU  - Alexander V. Bobylev
AU  - Sergey V. Meleshko
PY  - 2020
DA  - 2020/05/04
TI  - Group analysis of the generalized Burnett equations
JO  - Journal of Nonlinear Mathematical Physics
SP  - 494
EP  - 508
VL  - 27
IS  - 3
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2020.1757238
DO  - 10.1080/14029251.2020.1757238
ID  - Bobylev2020
ER  -