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Oscillations of a Stratified Liquid Partially Covered with Ice (General Case)

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Abstract

We study the problem of small motions of an ideal stratified liquid whose free surface consists of three regions: liquid surface without ice, a region of elastic ice, and a region of crumbled ice. The elastic ice is modeled by an elastic plate. The crumbled ice is understood as weighty particles of some matter floating on the free surface. Using the method of orthogonal projection of boundary conditions on a moving surface and the introduction of auxiliary problems, we reduce the original initial boundary value problem to an equivalent Cauchy problem for a second-order differential equation in a Hilbert space. We obtain conditions under which there exists a strong (with respect to time) solution of the initial boundary value problem describing the evolution of the hydrodynamic system under consideration.

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  1. “Mathematical Notes,”, Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, 119991, 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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Russian Text © The Author(s), 2020, published in Matematicheskie Zametki, 2020, Vol. 107, No. 1, pp. 130–144.

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Tsvetkov, D.O. Oscillations of a Stratified Liquid Partially Covered with Ice (General Case). Math Notes 107, 160–172 (2020). https://doi.org/10.1134/S0001434620010150

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  • DOI: https://doi.org/10.1134/S0001434620010150

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