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Journal of Mathematical Sciences

, Volume 236, Issue 6, pp 679–686 | Cite as

Vortex Steady Planar Entropic Flows of Ideal Gases

  • S. V. KhabirovEmail author
Article
  • 6 Downloads

Abstract

We find all solutions to the submodel of vortex, steady, planar, barotropic, entropic flows of an ideal gas and show that possible motions are exhausted by rectilinear motions under a constant pressure and motions along concentric circles. We present a group classification of the model of planar, vortex, entropic, nonbarotropic flows, examine invariant submodels, and propose a physical interpretation of certain solutions.

Keywords and phrases

vortex flow group analysis optimal system of subalgebras invariant solution 

AMS Subject Classification

37N10 76N15 76U05 

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References

  1. 1.
    G. G. Chernyi, Gas Dynamics [in Russian], Nauka, Moscow (1988).Google Scholar
  2. 2.
    S. V. Khabirov and Yu. A. Chirkunov, Elements of Symmetry Analysis of Differential Equations of Continuum Mechanics [in Russian], Novosibirks (2012).Google Scholar
  3. 3.
    L. V. Ovsyannikov, Lectures on the Fundamentals of Gas Dynamics [in Russian], Nauka, Moscow (1981).zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.R. R. Mavlutov Institute of MechanicsUfa Scientific Center of Russian Academy of SciencesUfaRussia

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