Skip to main content
Log in

Variational methods for pointwise stability of viscous fluid motions

  • Published:
Archive for Rational Mechanics and Analysis Aims and scope Submit manuscript

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

Access this article

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

Instant access to the full article PDF.

References

  1. Serrin, J., On the stability of viscous fluid motions, Arch. Rational Mech. Anal., 3, 1–13, (1959).

    Google Scholar 

  2. Joseph, D. D., Stability of Fluid Motions I, II, Berlin, Springer-Verlag, (1976).

    Google Scholar 

  3. Sattinger, D. H., The mathematical problem of hydrodynamic stability, Journal of Math. and Mech., 19, 797–817, (1970).

    Google Scholar 

  4. Prodi, G., Teoremi di tipo locale per il sistema di Navier-Stokes e stabilità delle soluzioni stazionarie, Rend. Sem. Mat. Univ. Padova, 32, 374–397, (1962).

    Google Scholar 

  5. Serrin, J., Interior estimates for solutions of the Navier-Stokes equations, Ed.: R. E. Langer, University of Wisconsin Press, pp. 376–378, (1963).

  6. Masuda, K., On the stability of incompressible viscous fluid motions past objects, Journal of the Math. Soc. of Japan, 27, 294–327, (1975).

    Google Scholar 

  7. Gerhardt, C., L p-estimates for solutions to the instationary Navier-Stokes equations in dimension two, Pacific J. Math., 79, 375–398, (1978).

    Google Scholar 

  8. Heywood, J. G.. The Navier-Stokes equations: on the existence, regularity and decay of solutions, Indiana Univ. Mat. J., 39, 639–681, (1980).

    Google Scholar 

  9. Leray, J., Sur le mouvement d'un liquide visqueux emplissant l'espace, Acta Math. 63, 193–248, (1934).

    Google Scholar 

  10. Galdi, G. P., Variational methods for stability of fluid motions in unbounded domains, Ricerche di Mat., 27, 387–404, (1978).

    Google Scholar 

  11. Serrin, J., The initial value problem for the Navier-Stokes equations, Ed.: R. E. Langer, University of Wisconsin Press, pp. 69–98, (1963).

  12. Ladyzhenskaya, O. A., The Mathematical Theory of Viscous Incompressible Flow, New York, Gordon & Breach, 1969.

    Google Scholar 

  13. Temam, R., Navier-Stokes Equations, Amsterdam, North-Holland, 1977.

    Google Scholar 

  14. Knops, R. J., and Wilkes, E. W., On Movchan's theorem for stability of continuous systems, Int. J. Engng. Sci., 4, 303–329, (1966).

    Google Scholar 

  15. Rionero, S., Metodi variazionali per la stabilità asintotica in media in magnetoidrodinamica, Ann. Mat. Pura App., 78, 339–364, (1968).

    Google Scholar 

  16. Kaniel, S., & Shinbrot, M., The initial value problem for Navier-Stokes equations, Arch. Rational Mech. Anal., 21, 270–285, (1966).

    Google Scholar 

  17. Cattabriga, L., Su un problema al contorno relativo al sistema di equazioni di Stokes, Rend. Sem. Univ. Padova, 31, 308–360, (1961).

    Google Scholar 

  18. Synge, J. L., On the stability of viscous liquid between two rotating coaxial cylinders, Proc. Roy. Soc. A 167, 250–254, (1938).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by J. Serrin

This work has been carried out under the auspices of the G. N. F. M. of the Italian C. N. R.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rosso, F. Variational methods for pointwise stability of viscous fluid motions. Arch. Rational Mech. Anal. 86, 181–195 (1984). https://doi.org/10.1007/BF00275733

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00275733

Keywords

Navigation