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Pis'ma v Zhurnal Èksperimental'noi i Teoreticheskoi Fiziki, 2019, Volume 110, Issue 7, Pages 443–448
DOI: https://doi.org/10.1134/S0370274X19190032 (Mi jetpl6011) 		 
This article is cited in 3 scientific papers (total in 3 papers)

PLASMA, HYDRO- AND GAS DYNAMICS

Algorithm for constructing exact solutions of the problem of unsteady plane motion of a fluid with a free surface

E. N. Zhuravlevaab, N. M. Zubarevcd, O. V. Zubarevac, E. A. Karabutab

a Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
b Novosibirsk State University, Novosibirsk, 630090 Russia
c Institute of Electrophysics, Ural Branch, Russian Academy of Sciences, Yekaterinburg, 620016 Russia
d Lebedev Physical Institute, Russian Academy of Sciences, Moscow, 119991 Russia
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DOI: https://doi.org/10.1134/S0370274X19190032
Abstract: Unsteady plane potential flows of an ideal incompressible fluid with a free surface in the absence of external forces and capillarity are studied. An algorithm to construct exact solutions for such flows has been proposed on the basis of the analysis of compatibility conditions of the equations of motion and an auxiliary complex transport equation. This algorithm makes it possible to significantly expand the list of known exact nontrivial solutions of the considered classical problem. This list has recently consisted of only a few Dirichlet solutions: flows for which the surface of the fluid is a parabola, ellipse, or hyperbola. This algorithm allows reproducing a recently found class of solutions specified by the Hopf equation for the complex velocity and finding a fundamentally new large class of solutions for which flows are described by the Hopf equation for the inverse complex velocity.
Funding agency Grant number
Russian Foundation for Basic Research 19-01-00096
19-08-00098
Russian Academy of Sciences - Federal Agency for Scientific Organizations 2
Ural Branch of the Russian Academy of Sciences 18-2-2-15
This work was supported by the Russian Foundation for Basic Research (project nos. 19-01-00096 and 19-08-00098), by the Presidium of the Russian Academy of Sciences (program no. 2), and by the Ural Branch of the Russian Academy of Sciences (project no. 18-2-2-15).
Received: 14.08.2019
Revised: 22.08.2019
Accepted: 23.08.2019
English version:
Journal of Experimental and Theoretical Physics Letters, 2019, Volume 110, Issue 7, Pages 452–456
DOI: https://doi.org/10.1134/S0021364019190135
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: E. N. Zhuravleva, N. M. Zubarev, O. V. Zubareva, E. A. Karabut, “Algorithm for constructing exact solutions of the problem of unsteady plane motion of a fluid with a free surface”, Pis'ma v Zh. Èksper. Teoret. Fiz., 110:7 (2019), 443–448; JETP Letters, 110:7 (2019), 452–456
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Письма в Журнал экспериментальной и теоретической физики Pis'ma v Zhurnal Иksperimental'noi i Teoreticheskoi Fiziki
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