Mathematical Study of the Small Oscillations of Two Nonmixing Fluids, the Lower Inviscid, the Upper Viscoelastic, in an Open Container

Essaouini, Hilal; Bakkali, Larbi El; Capodanno, P.

doi:10.1007/s00021-016-0300-7

Cited by 4 publications

(1 citation statement)

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“…At the same time, a number of methods based on functional analysis and the theory of operators in abstract Hilbert spaces are known in mathematical physics. As an example, we can cite the theory of quadratic operator beams, which is widely used in the study of various problems of mechanics and hydrodynamics related to the problem of small motions and normal oscillations (see, for example, [8][9][10][11][12][13][14][15][16][17][18]).…”

Section: Introductionmentioning

confidence: 99%

Analysis of the Oscillations of Stratified Liquid with Elastic Ice

Tsvetkov

2022

J. Adv. App. Comput. Math.

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We study the problem of small motions of an ideal stratified liquid with a free surface totally covered by an elastic ice. The elastic ice is modeled by an elastic plate. 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. We also study the spectrum of normal oscillations, the basic properties of the eigenfunctions.

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