On small motions and normal oscillations of a hydrosystem “a viscous fluid + a system of ideal fluids”

D. A. Zakora, N. D. Kopachevsky

Vernadskiy Tavricheskiy National University

Abstract: There is investigated a new problem on small motions and normal oscillations of a hydrodynamical system “a viscous fluid + a system of ideal fluids”. Existence conditions of strong solution of initial boundary value problem are obtained. For corresponding spectral problem asymptotic formulas for branches of eigenvalues are presented. Basisness properties of eigenelements are formulated.

MSC: 76D05, 58D30, 37N10, 58D25

Received: 30.11.2001

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