Open AccessSmall Motions of an Ideal Stratified Fluid in a Basin Covered with Ice
Author(s) -
Nikolay D. Kopachevsky,
D. O. Tsvetkov
Publication year - 2018
Publication title -
sovremennaâ matematika. fundamentalʹnye napravleniâ
Language(s) - English
Resource type - Journals
eISSN - 2949-0618
pISSN - 2413-3639
DOI - 10.22363/2413-3639-2018-64-3-573-590
Subject(s) - boundary value problem , surface (topology) , free surface , ideal (ethics) , boundary (topology) , free boundary problem , mathematics , mathematical analysis , hilbert space , perfect fluid , cauchy problem , initial value problem , space (punctuation) , mechanics , physics , geometry , mathematical physics , computer science , law , political science , operating system
We study the problem on small motions of an ideal stratied uid with a free surface partially covered with crushed ice. The crushed ice is supposed to be ponderable particles of some matter oating on the free surface. These particles do not interact with each other during oscillations of the free boundary (or this interaction is neglible) and stay on the surface during these oscillations. Using the method of orthogonal projecting of boundary-value conditions on the free surface and introducing auxiliary problems, we reduce the original initial-boundary value problem to the equivalent Cauchy problem for a second-order dierential equation in some 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 this hydraulic system.