N. M. Zubarev, E. A. Karabut, “Exact local solutions for the formation of singularities on the free surface of an ideal fluid”, Pis'ma v Zh. Èksper. Teoret. Fiz., 107:7 (2018), 434–439; JETP Letters, 107:7 (2018), 412

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Pis'ma v Zhurnal Èksperimental'noi i Teoreticheskoi Fiziki, 2018, Volume 107, Issue 7, Pages 434–439
DOI: https://doi.org/10.7868/S0370274X18070056 (Mi jetpl5537)

This article is cited in 28 scientific papers (total in 28 papers)

PLASMA, HYDRO- AND GAS DYNAMICS

Exact local solutions for the formation of singularities on the free surface of an ideal fluid

N. M. Zubarev^ab, E. A. Karabut^cd

^a Lebedev Physical Institute, Russian Academy of Sciences, Moscow, Russia
^b Institute of Electrophysics, Ural Branch, Russian Academy of Sciences, Yekaterinburg, Russia
^c Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia
^d Novosibirsk State University, Novosibirsk, Russia

Full-text PDF (196 kB) Citations (28)

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DOI: https://doi.org/10.7868/S0370274X18070056

Abstract: A classical problem of the dynamics of the free surface of an ideal incompressible fluid with infinite depth has been considered. It has been found that the regime of motion of the fluid where the pressure is a quadratic function of the velocity components is possible in the absence of external forces and capillarity. It has been shown that equations of plane potential flow for this situation are linearized in conformal variables and are then easily solved analytically. The found solution includes an arbitrary function specifying the initial shape of the surface of the fluid. The developed approach makes it possible for the first time to locally describe the formation of various singularities on the surface of the fluid—bubbles, drops, and cusps.

Funding agency	Grant number
Russian Foundation for Basic Research	17-08-00430_а 16-08-00228_а
Russian Academy of Sciences - Federal Agency for Scientific Organizations	2
Ural Branch of the Russian Academy of Sciences	18-2-2-15

Received: 29.01.2018
Revised: 12.02.2018

English version:
Journal of Experimental and Theoretical Physics Letters, 2018, Volume 107, Issue 7, Pages 412–417
DOI: https://doi.org/10.1134/S0021364018070135

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: N. M. Zubarev, E. A. Karabut, “Exact local solutions for the formation of singularities on the free surface of an ideal fluid”, Pis'ma v Zh. Èksper. Teoret. Fiz., 107:7 (2018), 434–439; JETP Letters, 107:7 (2018), 412–417

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https://www.mathnet.ru/eng/jetpl5537

https://www.mathnet.ru/eng/jetpl/v107/i7/p434

This publication is cited in the following 28 articles:

B G Konopelchenko, G Ortenzi, J. Phys. A: Math. Theor., 57:8 (2024), 085701
B. G. Konopelchenko, G. Ortenzi, Stud Appl Math, 152:1 (2024), 5
Evgenii Karabut, Elena Zhuravleva, Mathematics, 11:15 (2023), 3422
Nikolay M. Zubarev, Mathematics, 11:9 (2023), 1999
Konopelchenko B.G., Ortenzi G., J. Phys. A-Math. Theor., 55:3 (2022), 035203
E.A. Karabut, E.N. Zhuravleva, N.M. Zubarev, O.V. Zubareva, J. Fluid Mech., 953 (2022)
Yu. Gao, Yu. Gao, J.-G. Liu, Q. Appl. Math., 79:1 (2021), 55–102
S. A. Barengolts, K. E. Bobrov, N. M. Zubarev, O. V. Zubareva, IEEE Trans. Plasma Sci., 49:9 (2021), 2470–2477
A. I. Dyachenko, S. A. Dyachenko, P. M. Lushnikov, V. E. Zakharov, Proc. R. Soc. A-Math. Phys. Eng. Sci., 477:2249 (2021), 20200811
P. M. Lushnikov, V. E. Zakharov, Water Waves, 3:1 (2021), 251
E. N. Zhuravleva, N. M. Zubarev, O. V. Zubareva, E. A. Karabut, Dokl. Phys., 66:12 (2021), 348
E. N. Zhuravleva, N. M. Zubarev, O. V. Zubareva, E. A. Karabut, Theoret. and Math. Phys., 202:3 (2020), 344–351
N. M. Zubarev, E. A. Kochurin, Theoret. and Math. Phys., 202:3 (2020), 352–362
E. A. Karabut, E. N. Zhuravleva, Theoret. and Math. Phys., 202:3 (2020), 371–380
V. E. Zakharov, Theoret. and Math. Phys., 202:3 (2020), 285–294
E. A. Karabut, E. N. Zhuravleva, N. M. Zubarev, J. Fluid Mech., 890 (2020), A13
Olga Zubareva, Konstantin Bobrov, Nikolay Zubarev, 2020 7th International Congress on Energy Fluxes and Radiation Effects (EFRE), 2020, 232
A. I. Dyachenko, S. A. Dyachenko, P. M. Lushnikov, V. E. Zakharov, J. Fluid Mech., 874 (2019), PII S0022112019004488, 891–925
E. A. Kochurin, Tech. Phys. Lett., 45:2 (2019), 65–68
E. N. Zhuravleva, N. M. Zubarev, O. V. Zubareva, E. A. Karabut, JETP Letters, 110:7 (2019), 452–456

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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