Skip to main content
SpringerLink
Log in

Generalized fluid flows, their approximation and applications

  • Published:
Geometric & Functional Analysis GAFA Aims and scope Submit manuscript

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

References

  1. S. Alperin, Approximation to and by measure preserving homeomorphisms, J. of London Math. Soc. 18 (1978), 305–315.

    Google Scholar 

  2. V.I. Arnold, Sur la geometrie differentielle des groupes de Lie de dimension infinie et ces applications a l'hydrodynamiques des fluid parfaits, Ann. Inst. Fourier, Grenoble 16 (1966), 319–361.

    Google Scholar 

  3. A.M. Bloch, H. Flashka, T. Ratiu, A Schur-Horn-Kostant convexity theory for the diffeomorphism group of the annulus, Inventionnes Mathematica 113:3 (1993), 511–530.

    Google Scholar 

  4. Y. Brenier, The Least Action Principle and the related concept of generalized flows for incompressible perfect fluids, Journal of the American Mathematical Society 2:2 (1989).

    Google Scholar 

  5. Y. Brenier, A dual Least Action Principle for the motion of an ideal incompressible fluid, preprint November 1991, 1–30.

  6. D.G. Ebin, J. Mardsen, Groups of diffemorphisms and the motion of an ideal incompressible fluid, Ann. of Math. 92:2 (1970), 102–163.

    Google Scholar 

  7. Y. Eliashberg, T. Ratiu, The diameter of the symplectomorphism group is infinite, Invent. Math. 103 (1990), 327–370.

    Google Scholar 

  8. N. Grossman, Hilbert manifolds without epiconjugate points, Proc. Amer. Math. Soc. 16 (1965), 1365–1371.

    Google Scholar 

  9. G. Misiolek, Conjugate points inD μ(Ti), Preprint, November 1993.

  10. J. Moser, On the volume element on a manifold. Trans. Amer. Math. Soc. 120 (1965), 286–294.

    Google Scholar 

  11. J. Moser, Remark on the smooth approximation of volume-preserving home-omorphisms by symplectic diffeomorphisms, Zürich Forschungsinst. für Mathematik ETH, preprint, October 1992.

  12. Yu.A. Neretin, Categories of bistochastic measures, and representations of some infinite-dimensional groups, Russian Acad. Sci. Sb. Math. 75:1 (1993), 197–219.

    Google Scholar 

  13. A.I. Shnirelman, On the geometry of the group of diffeomorphisms and the dynamics of an ideal incompressible fluid, Math. USSR Sbornik 56:1 (1987), 79–105, 1–30.

    Google Scholar 

  14. A.I. Shnirelman, Attainable diffeomorphisms, Geometric And Functional Analysis 3:3 (1993), 279–294.

    Article  Google Scholar 

  15. A.I. Shnirelman, Lattice theory and the flows of ideal incompressible fluid, Russian Journal of Mathematical Physics 1:1 (1993), 105–114.

    Google Scholar 

  16. A.M. Vershik, Multivalued mappings with invariant measure and the Markov operators (in Russian), Zapiski Nauchnykh Seminarov LOMI, Leningrad 72 (1977), 121–160.

    Google Scholar 

  17. L.C. Young, Lectures on the calculus of variations and optimal control theory, Chelsea, 1980, New York.

Download references

Author information

Authors and Affiliations

  1. School of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel Aviv University, 69978, Tel Aviv, Israel

    A. I. Shnirelman

Authors
  1. A. I. Shnirelman
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shnirelman, A.I. Generalized fluid flows, their approximation and applications. Geometric and Functional Analysis 4, 586–620 (1994). https://doi.org/10.1007/BF01896409

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01896409

Keywords

Search

Navigation