Skip to main content
SpringerLink
Log in

Nonstationary version of Zhikov’s compensated compactness lemma and its application to the solvability of the generalized Navier-Stokes equations

  • Mathematics
  • Published:
Doklady Mathematics 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. L. Tartar, Homogénéisation: Cours Peccot au College de France (Paris, 1977).

  2. F. Murat, Ann. Scuola Norm. Super. Pisa. Cl. Sci. Fis. Mat. 5, 489–507.

  3. V. V. Zhikov, Dokl. Math. 77, 383–387 (2008) [Dokl. Akad. Nauk 420, 300–305 (2008)].

    Article  MATH  Google Scholar 

  4. V. V. Zhikov, Funkts. Anal. Ego Prilozh. 43(2), 19–38 (2009).

    MathSciNet  Google Scholar 

  5. V. V. Zhikov and S. E. Pastukhova, Mat. Sb. 199(12), 19–52 (2008).

    MathSciNet  Google Scholar 

  6. V. V. Zhikov, Funkts. Anal. Ego Prilozh. 43(3), 33–53 (2009).

    MathSciNet  Google Scholar 

  7. O. A. Ladyzhenskaya, Tr. Mat. Inst. Akad. Nauk SSSR 102, 85–104 (1967).

    MATH  Google Scholar 

  8. J.-L. Lions, Quelques méthodes de résolution des problémes aux limites non linéires (Dunod, Paris, 1969; Mir, Moscow, 1972).

    Google Scholar 

  9. P. Billingsley, Convergence of Probability Measures (Wiley, New York, 1968; Nauka, Moscow, 1977).

    MATH  Google Scholar 

  10. M. Ruižička, Electrorheological Fluids: Modeling and Mathematical Theory (Springer-Verlag, Berlin, 2000).

    Google Scholar 

  11. V. V. Zhikov, Dokl. Akad. Nauk 345, 10–14 (1995).

    MathSciNet  Google Scholar 

  12. V. V. Zhikov, Zap. Nauchn. Semin. POMI 30, 285–299 (2004).

    Google Scholar 

  13. H. Bellout, F. Bloom, and J. Nečas, Commun. PDE 19(11/12), 1763–1803 (1994).

    Article  MATH  Google Scholar 

  14. J. Malék, J. Ne as, and M. Ružička, Math. Models Methods Appl. Sci. 3(1), 35–63 (1993).

    Article  MathSciNet  MATH  Google Scholar 

  15. J. Malék, J. Ne as, M. Rokyta, and M. Ružička, Weak and Measure-Valued Solutions to Evolutionary PDEs (Chapman and Hall, London, 1996).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Moscow State Institute of Radio Engineering, Electronics, and Automation (Technical University), pr. Vernadskogo 78, Moscow, 119454, Russia

    S. E. Pastukhova

Authors
  1. S. E. Pastukhova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. E. Pastukhova.

Additional information

Original Russian Text © S.E. Pastukhova, 2010, published in Doklady Akademii Nauk, 2010, Vol. 430, No. 4, pp. 448–453.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pastukhova, S.E. Nonstationary version of Zhikov’s compensated compactness lemma and its application to the solvability of the generalized Navier-Stokes equations. Dokl. Math. 81, 66–71 (2010). https://doi.org/10.1134/S1064562410010199

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1064562410010199

Keywords

Search

Navigation