Initial-boundary value problem for the equations of dynamics of a rotating viscous stratified fluid

D. O. Tsvetkov

Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 33 (2023) no. 4, pp. 625-641

Résumé

We study the problem of small motions of a viscous stratified fluid partially filling a container that uniformly rotates around an axis co-directed by gravity. The problem is studied on the basis of an approach related to the application of the so-called operator matrix theory. To this end, we introduce Hilbert spaces and some their subspaces, as well as auxiliary boundary value problems. The original initial-boundary value problem is reduced to the Cauchy problem for a first-order differential equation in some Hilbert space. After a detailed study of the properties of the operator coefficients corresponding to the resulting system of equations, we prove a theorem on the solvability of the Cauchy problem. On this basis, we find sufficient conditions for the existence of a solution of the original initial-boundary value problem describing the evolution of the hydro-system.

Détail

Keywords: stratification effect in viscous fluids, differential equation in Hilbert space, Cauchy problem

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