Skip to main content
Log in

Spectral properties of operators for the systems of hydrodynamics of a rotating liquid and nonuniqueness of the limit amplitude

  • Published:
Siberian Mathematical Journal 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.

Literature Cited

  1. S. L. Sobolev, “On the motion of a symmetric top with a cavity filled with liquid,” Zh. Prikl. Mekh. Tekh. Fiz., No. 3, 20–55 (1960).

    Google Scholar 

  2. S. L. Sobolev, “On a new problem of mathematical physics,” Izv. Akad. Nauk SSSR, Ser. Mat.,18, No. 1, 3–50 (1954).

    Google Scholar 

  3. R. A. Aleksandryan, Yu. M. Berezanskii, V. A. Il'in, and A. G. Kostyuchenko, “Certain problems of the spectral theory for partial differential equations,” in: Partial Differential Equations [in Russian], Nauka, Moscow (1970), pp. 3–35.

    Google Scholar 

  4. A. A. Dezin and V. N. Maslennikova, “Nonclassical boundary-value problems,” ibid., 81–95.

    Google Scholar 

  5. T. I. Zelenyak and V. P. Mikhailov, “Asymptotic behavior of solutions of some boundary-value problems in mathematical physics as t→∞,” ibid., 96–118.

    Google Scholar 

  6. V. N. Maslennikova, “A mathematical study of rotating liquid hydrodynamics,” in: The National Conference on Partial Differential Equations [in Russian], Moscow State Univ. (1977), pp. 153–156.

  7. A. A. Dezin, T. I. Zelenyak, and V. N. Maslennikova, “On certain mathematical problems in hydrodynamics,” in: Partial Differential Equations [in Russian], Nauka, Novosibirsk (1980), pp. 21–31.

    Google Scholar 

  8. G. V. Demidenko, V. G. Perepelkin, S. V. Uspenskii, and S. I. Yanov, “Boundary-value problems for equations and systems of Sobolev type,” in: Partial Differential Equations [in Russian], Nauka, Novosibirsk (1986), pp. 72–84.

    Google Scholar 

  9. G. I. Marchuk, Numerical Solution of the Problems of Atmosphere and Ocean Dynamics [in Russian], Gidrometeoizdat, Leningrad (1974).

    Google Scholar 

  10. V. V. Penenko and A. E. Aloyan, Models and Methods for Solving Environment Protection Problems [in Russian], Nauka, Novosibirsk (1985).

    Google Scholar 

  11. L. M. Brekhovskikh and V. V. Goncharov, Introduction to Mechanics of Continua [in Russian], Nauka, Moscow (1982).

    Google Scholar 

  12. V. N. Maslennikova and Pal Prodip Kumar, “On stabilization and limit amplitude of a solution to the Cauchy problem for nonhomogeneous Sobolev systems,” Sib. Mat. Zh.,27, No. 3, 142–153 (1986).

    Google Scholar 

  13. F. Riesz and B. Szokefalvi-Nagy, Lectures in Functional Analysis [Russian translation], Mir, Moscow (1979).

    Google Scholar 

  14. T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, New York (1966).

    Google Scholar 

  15. M. E. Bogovskii, “Decomposition ofL 2(Ω;R n) into the direct sum of the subspaces of solenoidal and potential vector fields,” Sov. Math. Dokl.,33, No. 1, 161–165 (1986).

    Google Scholar 

  16. J. V. Ralston, “On stationary modes in inviscid rotating fluids,” J. Math. Anal. Appl.,44, 366–383 (1973).

    Google Scholar 

  17. S. L. Sobolev, Applications of Functional Analysis in Mathematical Physics [in Russian], Nauka, Novosibirsk (1962).

    Google Scholar 

  18. P. K. Pal and V. N. Maslennikova, “Spectral properties of operators in the problem of the oscillation of a compressible fluid in rotating containers,” Sov. Math. Dokl.,31, No. 2, 318–322 (1985).

    Google Scholar 

  19. S. Agmon, A. Douglis, and L. Nirenberg, “Estimates near the boundary for solutions of elliptic differential equations,” Commun. Pure Appl. Math.,17, 35–92 (1964).

    Google Scholar 

  20. G. Grubb and G. Geymonat, “The essential spectrum of elliptic systems of mixed order,” Math. Ann.,227, 257–276 (1977).

    Google Scholar 

  21. G. Talenti, “Spectrum of the Laplace operator acting inL p (R n),” Symposia Mathematica Instituto Nazionale di Alta Mathematica,7 (1971).

Download references

Authors

Additional information

Dedicated to the 80th birthday of Sergei L'vovich Sobolev.

Moscow. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 29, No. 5, pp. 157–171, September–October, 1988.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Maslennikova, V.N., Giniatullin, A.I. Spectral properties of operators for the systems of hydrodynamics of a rotating liquid and nonuniqueness of the limit amplitude. Sib Math J 29, 812–824 (1988). https://doi.org/10.1007/BF00970278

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00970278

Keywords

Navigation