Geodesic
On an initial-boundary value problem arising in the dynamics
Čelâbinskij fiziko-matematičeskij žurnal, Tome 4 (2019) no. 2, pp. 179-198

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A linearized problem of small motions of a system of layers of incompressible ideal stratified fluids with a free surface, covered with the elastic ice that is modeled by the elastic plate, is considered. With using the method of the orthogonal projecting the boundary conditions on the moving surface, the original initial-boundary value problem is reduced to the equivalent Cauchy problem for an ordinary differential equation of the second order in some Hilbert space. We find the conditions under which there exists a time-strong solution to the initial-boundary value problem describing the evolution of the original hydrodynamics system.
Keywords: stratified fluid, elastic ice, differential-operator equation, the Cauchy problem in a Hilbert space, strong solution. 
@article{CHFMJ_2019_4_2_a4,
     author = {D. O. Tsvetkov},
     title = {On an initial-boundary value problem arising in the dynamics},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {179--198},
     publisher = {mathdoc},
     volume = {4},
     number = {2},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2019_4_2_a4/}
}
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D. O. Tsvetkov. On an initial-boundary value problem arising in the dynamics. Čelâbinskij fiziko-matematičeskij žurnal, Tome 4 (2019) no. 2, pp. 179-198. http://geodesic.mathdoc.fr/item/CHFMJ_2019_4_2_a4/