Geodesic
Oscillations of stratified liquid partially covered by crumpling ice
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2018), pp. 70-85

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We study the problem on small motions of ideal stratified fluid with a free surface, partially covered by crumbling ice. By the method of orthogonal projecting the boundary conditions on the moving surface and the introduction of auxiliary problems of the original initial-boundary value problem is reduced to the equivalent Cauchy problem for a differential equation of the second order in a Hilbert space. We find sufficient existence conditions for a strong (with respect to the time variable) solution to the initial-boundary value problem describing the evolution of the specified hydrodynamics system.
Keywords: stratification effect in ideal fluids, initial boundary value problem, differential equation in Hilbert space, Cauchy problem, strong solution. 
@article{IVM_2018_12_a4,
     author = {D. O. Tsvetkov},
     title = {Oscillations of stratified liquid partially covered by crumpling ice},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {70--85},
     publisher = {mathdoc},
     number = {12},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2018_12_a4/}
}
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D. O. Tsvetkov. Oscillations of stratified liquid partially covered by crumpling ice. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2018), pp. 70-85. http://geodesic.mathdoc.fr/item/IVM_2018_12_a4/