Skip to main content
SpringerLink
Log in

On Navier-Stokes fields with linear vorticity

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We describe all Navier-Stokes fields with vorticity linear in space variables.

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. V. I. Fushchich, V. M. Shtelen', and N. I. Serov, Symmetry Analysis and Exact Solutions of Nonlinear Equations of Mathematical Physics [in Russian], Naukova Dumka, Kiev (1989).

    MATH  Google Scholar 

  2. A. F. Sidorov, V. P. Shapelev, and N. N. Yanenko, Method of Differential Constraints and Its Applications in Gas Dynamics [in Russian], Nauka, Novosibirsk (1984).

    Google Scholar 

  3. Yu. A. Danilov, Group Properties of Maxwell and Navier-Stokes Equations [in Russian], Preprint, Institute of Atomic Energy, Academy of Sciences of the USSR (1967).

  4. V. O. Bytev, “Group properties of the Maxwell and Navier-Stokes equations,” in: Chisl. Metody Mekh. Splosh. Sredy, 3, No. 4 13–14 (1972).

  5. S. P. Lloyd, “The infinitesimal group of the Navier-Stokes equations,” Acta Mech., 38, No. 1-2, 85–98 (1981).

    Article  MATH  MathSciNet  Google Scholar 

  6. W. I. Fushchych, W. M. Shtelen, and S. L. Slavutskiy, “Reduction and exact solutions of the Navier-Stokes equations,” J. Phys. A, Math. Gen., 24, No. 4, 971–984 (1991).

    Article  Google Scholar 

  7. L. V. Ovsyannikov, Group Analysis of Differential Equations [in Russian], Nauka, Moscow (1978).

    MATH  Google Scholar 

  8. W. I. Fushchych and R. O. Popowych, “Symmetry reduction and exact solutions of the Navier-Stokes equations,” J. Nonlin. Math. Phys., 1, No. 2, 75–113 (1994), 1, No. 2, 158–188 (1994).

    Article  MATH  Google Scholar 

Download references

Authors
  1. G. V. Popovich
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. O. Popovich
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 9, pp. 1223–1229, September, 1997.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Popovich, G.V., Popovich, R.O. On Navier-Stokes fields with linear vorticity. Ukr Math J 49, 1377–1385 (1997). https://doi.org/10.1007/BF02487345

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02487345

Keywords

Search

Navigation