Advertisement

Siberian Mathematical Journal

, Volume 44, Issue 5, pp 857–866 | Cite as

Symmetry of the Barochronous Motions of a Gas

  • L. V. Ovsyannikov
Article

Abstract

We study the system of nonlinear differential equations which expresses the constancy of the algebraic invariants of the Jacobian matrix for smooth vector fields in three-dimensional space. This system is equivalent to the equations of gas dynamics which describe the barochronous motions of a gas (the pressure and density depend only on the time). We present the results of computation of the admissible local Lie group and construction of the general solution of the system. We mention a few new problems that arise here.

admissible local Lie group of transformations algebra of Lie operators equivalence general solution 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Chupakhin A. P., "On the barochronous motions of a gas," Dokl. Akad. Nauk, 352, No. 5, 624–626 (1997).Google Scholar
  2. 2.
    Ovsyannikov L. V., Group Analysis of Diffirential Equations [in Russian], Nauka, Moscow (1978).Google Scholar
  3. 3.
    Ovsyannikov L. V., "Isobaric motions of a gas," Differentsial'nye Uravneniya, 30, No. 10, 1792–1799 (1994).Google Scholar

Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • L. V. Ovsyannikov
    • 1
  1. 1.Lavrent'ev Institute of HydrodynamicsNovosibirsk

Personalised recommendations