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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2021, Volume 27, Number 1, Pages 173–187
DOI: https://doi.org/10.21538/0134-4889-2021-27-1-173-187
(Mi timm1801)
 

This article is cited in 1 scientific paper (total in 1 paper)

Motion of gas particles based on the Galilei group

S. V. Khabirov

Mavlyutov Institute of Mechanics, Ufa Centre of the Russian Academy of Sciences
Full-text PDF (230 kB) Citations (1)
References:
Abstract: Invariants of the Galilei group determine the invariant and partially invariant solutions of continuum mechanics equations. Invariant motions have a point density collapse with straight world lines. The invariant characteristics of the equations of gas dynamics, which can be used to construct weak solutions with a discontinuity of the derivatives, are considered. Partially invariant solutions with a linear velocity field are investigated for special gas equations; such solutions are regular. There are possible solutions with a point collapse at an infinitely distant point. A classification of such solutions is given for the state equations from the group classification of the gas dynamics equations. The motion of gas particles for such solutions occurs along curvilinear trajectories to a point collapse or from a point source. The classification uses the method of separation of variables in the equation for functions of different independent variables. The same motion of gas particles is possible for different equations of state.
Keywords: gas dynamics, Galilei group, partially invariant solutions, linear field of velocities, point collapse, state equation, method of separation of variables.
Funding agency Grant number
Russian Foundation for Basic Research 18-29-10071
Ministry of Science and Higher Education of the Russian Federation 0246-2019-0052
This work was supported by the Russian Foundation for Basic Research (project no. 18-29-10071) and within the State Assignment no. 0246-2019-0052.
Received: 25.12.2020
Revised: 08.02.2021
Accepted: 15.02.2021
Bibliographic databases:
Document Type: Article
UDC: 517.958:533.7
MSC: 76M60, 76N15, 35Q70
Language: Russian
Citation: S. V. Khabirov, “Motion of gas particles based on the Galilei group”, Trudy Inst. Mat. i Mekh. UrO RAN, 27, no. 1, 2021, 173–187
Citation in format AMSBIB
\Bibitem{Kha21}
\by S.~V.~Khabirov
\paper Motion of gas particles based on the Galilei group
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2021
\vol 27
\issue 1
\pages 173--187
\mathnet{http://mi.mathnet.ru/timm1801}
\crossref{https://doi.org/10.21538/0134-4889-2021-27-1-173-187}
\elib{https://elibrary.ru/item.asp?id=44827404}
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  • https://www.mathnet.ru/eng/timm/v27/i1/p173
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Trudy Instituta Matematiki i Mekhaniki UrO RAN
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    Abstract page:114
    Full-text PDF :30
    References:23
    First page:2
     
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