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Sibirskii Matematicheskii Zhurnal, 2016, Volume 57, Number 1, Pages 126–156
DOI: https://doi.org/10.17377/smzh.2016.57.111 (Mi smj2734) 		 
Unique solvability of the water waves problem in Sobolev spaces

V. I. Nalimov

Lavrentyev Institute of Hydrodynamics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
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DOI: https://doi.org/10.17377/smzh.2016.57.111
Abstract: Studying the problem of unsteady waves on the surface of an infinitely deep heavy incompressible ideal fluid, we derive equations for the height of the free surface as well as the vertical and horizontal components of velocity on the free surface. We prove that the initial-boundary value water waves problem is short-time solvable in Sobolev spaces.
Keywords: water waves, unique solvability, Dirichlet–Neumann operator.
Received: 16.03.2015
English version:
Siberian Mathematical Journal, 2016, Volume 57, Issue 1, Pages 97–123
DOI: https://doi.org/10.1134/S0037446616010110
Bibliographic databases:
Document Type: Article
UDC: 517.958
Language: Russian
Citation: V. I. Nalimov, “Unique solvability of the water waves problem in Sobolev spaces”, Sibirsk. Mat. Zh., 57:1 (2016), 126–156; Siberian Math. J., 57:1 (2016), 97–123
Citation in format AMSBIB
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    		Сибирский математический журнал Siberian Mathematical Journal
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