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Teoreticheskaya i Matematicheskaya Fizika, 2020, Volume 202, Number 3, Pages 425–436
DOI: https://doi.org/10.4213/tmf9791 (Mi tmf9791) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Construction of exact solutions of the problem of the motion of a fluid with a free boundary using infinite systems of differential equations

E. A. Karabutab, E. N. Zhuravlevaab

a Lavrentiev Institute for Hydrodynamics, Siberian Branch of RAS, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia
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DOI: https://doi.org/10.4213/tmf9791
Abstract: We consider the well-known hydrodynamics problem for the planar potential motion of an ideal incompressible fluid with a free boundary without capillarity and propose a method for finding exact solutions based on reducing the boundary-value problems to systems of ordinary differential equations. We obtain two examples of flows: a stationary motion of a heavy fluid over a smooth bottom and a nonstationary motion of a fluid that originally filled a wedge.
Keywords: ideal incompressible fluid, exact solution, conformal map, doubly periodic function.
Funding agency Grant number
Russian Foundation for Basic Research 19-01-00096
This research is supported by the Russian Foundation for Basic Research (Grant No. 19-01-00096).
Received: 17.08.2019
Revised: 03.10.2019
English version:
Theoretical and Mathematical Physics, 2020, Volume 202, Issue 3, Pages 371–380
DOI: https://doi.org/10.1134/S004057792003006X
Bibliographic databases:
Document Type: Article
MSC: 30C35
Language: Russian
Citation: E. A. Karabut, E. N. Zhuravleva, “Construction of exact solutions of the problem of the motion of a fluid with a free boundary using infinite systems of differential equations”, TMF, 202:3 (2020), 425–436; Theoret. and Math. Phys., 202:3 (2020), 371–380
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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