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Doklady Physics

, Volume 62, Issue 4, pp 213–217 | Cite as

On the evolution of a finite volume of ideal incompressible fluid with a free surface

  • V. N. BelykhEmail author
Mechanics

Abstract

The local existence and uniqueness theorem for a time-analytical solution to the problem in a precise mathematical formulation has been proven by assuming the fluid motion to be potential.

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References

  1. 1.
    L. V. Ovsyannikov, Dokl. Akad. Nauk SSSR 163 (4), 819 (1965).MathSciNetGoogle Scholar
  2. 2.
    L. V. Ovsyannikov, General Equations and Examples, in A Problem on the Unsteady Motion of a Fluid with a Free Boundary (Nauka, Novosibirsk, 1967), pp. 3–75 [in Russian].Google Scholar
  3. 3.
    V. I. Nalimov, in Continuum Dynamics (Novosibirsk, 1969), Issue 1, pp. 258–263 [in Russian].Google Scholar
  4. 4.
    V. I. Nalimov, in Continuum Dynamics (Novosibirsk, 1974), Issue 18, pp. 104–210 [in Russian]Google Scholar
  5. 5.
    L. V. Ovsyannikov, N. I. Makarenko, V. I. Nalimov, et al., Nonlinear Problems of the Theory of Surface and Internal Waves (Nauka, Novosibirsk, 1985) [in Russian].Google Scholar
  6. 6.
    C. Bardos and E. S. Titi, Usp. Mat. Nauk 62 (3), 3 (2007).CrossRefGoogle Scholar
  7. 7.
    W. Craig and C. E. Wayne, Usp. Mat. Nauk 62 (3), 95 (2007).CrossRefGoogle Scholar
  8. 8.
    A. I. Dyachenko and V. E. Zakharov, Pis’ma Zh. Eksp. Teor. Fiz. 88, 356 (2008).Google Scholar
  9. 9.
    V. I. Nalimov, Sib. Mat. Zhurnal 54 (2), 355 (2013).MathSciNetGoogle Scholar
  10. 10.
    E. A. Karabut and E. N. Zhuravleva, Dokl. Akad. Nauk 469 (3), 295 (2016).Google Scholar
  11. 11.
    A. I. Dyachenko, D. I. Kachulin, and V. E. Zakharov, Pis’ma Zh. Eksp. Teor. Fiz. 102, 295 (2015).Google Scholar
  12. 12.
    L. V. Ovsyannikov, in Continuum Dynamics (Novosibirsk, 1971), Issue 8, pp. 22–26 [in Russian].Google Scholar
  13. 13.
    V. N. Belykh, in Continuum Dynamics (Novosibirsk, 1972), Issue 12, pp. 63–76 [in Russian].Google Scholar
  14. 14.
    L. V. Ovsyannikov, Trudy Matematicheskogo Instituta im. V.A. Steklova 281, 7 (2013).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsRussian Academy of Sciences, Siberian BranchNovosibirskRussia

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