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Oscillations of Stratified Liquid Partially Covered by Crumpling Ice

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Abstract

We study the problem on small motions of ideal stratified fluid with a free surface, partially covered by crumbling ice. By the method of orthogonal projecting the boundary conditions on the moving surface and, with the help of investigation of some auxiliary problems, the original initial-boundary value problem is reduced to the equivalent Cauchy problem for a second order differential equation in a Hilbert space. We find sufficient existence conditions for existence of a strong (with respect to the time variable) solution to the initial-boundary value problem describing evolution of the specified hydrodynamics system.

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Authors and Affiliations

  1. V. I. Vernadsky Crimean Federal University (Taurida Academy), pr. Vernadskogo 4, Simferopol, 295000, Russia

    D. O. Tsvetkov

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  1. D. O. Tsvetkov
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Correspondence to D. O. Tsvetkov.

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Original Russian Text © D.O. Tsvetkov, 2018, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2018, No. 12, pp. 70–85.

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Tsvetkov, D.O. Oscillations of Stratified Liquid Partially Covered by Crumpling Ice. Russ Math. 62, 59–73 (2018). https://doi.org/10.3103/S1066369X18120058

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  • DOI: https://doi.org/10.3103/S1066369X18120058

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