Skip to main content
SpringerLink
Log in

Investigation of the geodesic flow on an infinite-dimensional Lie group by means of the coadjoint action operator

  • Published:
Proceedings of the Steklov Institute of Mathematics Aims and scope Submit manuscript

Abstract

We consider a representation of the Euler equations as the geodesic flow on an infinite-dimensional Lie group. In these terms, we establish properties of solutions, which are provided by local existence and uniqueness theorems, at a limit point.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. M. Lukatsky, “Group Approach to Dynamics of a Continuous Medium,” Nauchn. Vestn. Mosk. Gos. Tekh. Univ. Grazhdanskoi Aviatsii, No. 100, 114–121 (2006).

  2. A. M. Lukatsky, “Group Approach to Dynamics of an Incompressible Fluid,” Nauchn. Vestn. Mosk. Gos. Tekh. Univ. Grazhdanskoi Aviatsii, Ser. Mat. Fiz., No. 114, 42–49 (2007).

  3. V. I. Arnold and B. A. Khesin, Topological Methods in Hydrodynamics (Springer, New York, 1998), Appl. Math. Sci. 125.

    MATH  Google Scholar 

  4. D. G. Ebin and J. Marsden, “Groups of Diffeomorphisms and the Motion of an Incompressible Fluid,” Ann. Math. 92, 102–163 (1970).

    Article  MathSciNet  Google Scholar 

  5. J. E. Marsden and M. McCracken, The Hopf Bifurcation and Its Applications (Springer, New York, 1976).

    MATH  Google Scholar 

  6. A. M. Lukatsky, “Group Approach to Dynamics of a Continuous Medium,” in Differential Equations and Related Questions: Abstr. Int. Conf. Dedicated to the Memory of I.G. Petrovskii, Moscow, May 21–26, 2007 (Moscow State Univ., Moscow, 2007), p. 178.

    Google Scholar 

  7. A. M. Lukatsky, “Investigation of the Geodesic Flow on the Group of Volume-Preserving Diffeomorphisms by Means of the Coadjoint Action Operator,” in Analysis and Singularities: Abstr. Int. Conf. Dedicated to the 70th Birthday of V.I. Arnold, Moscow, Aug. 20–24, 2007 (Steklov Math. Inst., Moscow, 2007), pp. 72–74.

    Google Scholar 

  8. B. A. Khesin, “Topological Fluid Dynamics,” Not. Am. Math. Soc. 52, 9–19 (2005).

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Energy Research Institute, Russian Academy of Sciences, ul. Nagornaya 31, kor. 2, Moscow, 117186, Russia

    A. M. Lukatsky

Authors
  1. A. M. Lukatsky
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Dedicated to Vladimir Igorevich Arnold with profound respect

Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2009, Vol. 267, pp. 204–213.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lukatsky, A.M. Investigation of the geodesic flow on an infinite-dimensional Lie group by means of the coadjoint action operator. Proc. Steklov Inst. Math. 267, 195–204 (2009). https://doi.org/10.1134/S0081543809040166

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0081543809040166

Keywords

Search

Navigation