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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
Full-text PDF (387 kB) Citations (1)
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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:
    1. T. Krasnoslobodzeva, M. Skvortsova, “Long wave dynamics in heavy wave gravitating fluid in Vlasov type model”, Networked Control Systems for Connected and Automated Vehicles, Lecture Notes in Networks and Systems, 510, 2023, 975  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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