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On the spectral criterion of stability in the problem of small motions of an ideal capillary fluid with disconnected free surface

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Abstract

This paper deals with the problem of static stability of the equilibrium state and the problem of stability of small (linear) movements of an ideal incompressible fluid in the open vessel with holes in the bottom. The gravitational forces and the surface tension are taken into account. We consider a case where the equilibrium surface of the fluid is curvilinear and corresponds to an arbitrary contact angle. Using the operator approach, we obtain the sufficient conditions for static and dynamic stabilities and propose a method of determination of the equilibrium surface.

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Authors and Affiliations

  1. Faculty of Mathematics and Informatics, V. I. Vernadsky Taurida National University, 4, Academician Vernadsky Prosp., Simferopol, 95007, Russia

    Nikolay D. Kopachevsky

  2. Faculty of Informatics, Crimea Engineering-Pedagogical University, 8, Uchebnyi L., Sevastopol’skaya Str., Simferopol, 95015, Russia

    Zera Z. Sitshayeva

Authors
  1. Nikolay D. Kopachevsky
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  2. Zera Z. Sitshayeva
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Correspondence to Nikolay D. Kopachevsky.

Additional information

Translated from Ukrains’ki˘ı Matematychny˘ı Visnyk, Vol. 11, No. 3, pp. 340–365, July–August, 2014.

Translated from Russian by V. V. Kukhtin

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Kopachevsky, N.D., Sitshayeva, Z.Z. On the spectral criterion of stability in the problem of small motions of an ideal capillary fluid with disconnected free surface. J Math Sci 206, 39–57 (2015). https://doi.org/10.1007/s10958-015-2292-x

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  • DOI: https://doi.org/10.1007/s10958-015-2292-x

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