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Teoreticheskaya i Matematicheskaya Fizika, 2020, Volume 202, Number 3, Pages 393–402
DOI: https://doi.org/10.4213/tmf9783 (Mi tmf9783) 		 
This article is cited in 1 scientific paper (total in 1 paper)

A new class of exact solutions in the planar nonstationary problem of motion of a fluid with a free boundary

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

a Lavrentiev Institute for Hydrodynamics, Siberian Branch of RAS, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia
c Institute for Electrophysics, Ural Branch of RAS, Yekaterinburg, Russia
d Lebedev Physical Institute, RAS, Moscow, Russia
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DOI: https://doi.org/10.4213/tmf9783
Abstract: We consider the classical problem of potential unsteady flow of an ideal incompressible fluid with a free boundary. It was previously discovered that in the absence of external forces and capillarity, a wide class of exact solutions of the problem can be described by the Hopf equation for a complex velocity. We here obtain a new class of solutions described by the Hopf equation for a quantity that is the inverse of the complex velocity. These solutions describe the evolution of two-dimensional perturbations of the free boundary in compression or expansion of a circular cavity (in the unperturbed state) in the fluid.
Keywords: ideal incompressible fluid, unsteady planar flow with a free boundary, exact solution, complex velocity, Hopf equation.
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 research is supported in part by the Russian Foundation for Basic Research (Grant Nos. 19-01-00096 and 19-08-00098), the Presidium of the Russian Academy of Sciences (Program 2), and the Ural Branch of the Russian Academy of Sciences (Project No. 18-2-2-15).
Received: 26.07.2019
Revised: 26.07.2019
English version:
Theoretical and Mathematical Physics, 2020, Volume 202, Issue 3, Pages 344–351
DOI: https://doi.org/10.1134/S0040577920030095
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: E. N. Zhuravleva, N. M. Zubarev, O. V. Zubareva, E. A. Karabut, “A new class of exact solutions in the planar nonstationary problem of motion of a fluid with a free boundary”, TMF, 202:3 (2020), 393–402; Theoret. and Math. Phys., 202:3 (2020), 344–351
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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