A. V. Yurov, A. A. Yurova, “One method for constructing exact solutions of equations of two-dimensional hydrodynamics of an incompressible fluid”, TMF, 147:1 (2006), 64–72; Theoret. and Math. Phys., 147:1 (2006), 501

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Teoreticheskaya i Matematicheskaya Fizika, 2006, Volume 147, Number 1, Pages 64–72
DOI: https://doi.org/10.4213/tmf2023 (Mi tmf2023)

This article is cited in 9 scientific papers (total in 9 papers)

One method for constructing exact solutions of equations of two-dimensional hydrodynamics of an incompressible fluid

A. V. Yurov^a, A. A. Yurova^b

^a Immanuel Kant State University of Russia
^b Kaliningrad State University

Full-text PDF (224 kB) Citations (9)

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DOI: https://doi.org/10.4213/tmf2023

Abstract: We propose a simple algebraic method for constructing exact solutions of equations of two-dimensional hydrodynamics of an incompressible fluid. The problem reduces to consecutively solving three linear partial differential equations for a nonviscous fluid and to solving three linear partial differential equations and one first-order ordinary differential equation for a viscous fluid.

Keywords: two-dimensional incompressible fluid, exact solutions.

Received: 12.07.2005
Revised: 21.10.2005

English version:
Theoretical and Mathematical Physics, 2006, Volume 147, Issue 1, Pages 501–508
DOI: https://doi.org/10.1007/s11232-006-0057-x

Bibliographic databases:

Language: Russian

Citation: A. V. Yurov, A. A. Yurova, “One method for constructing exact solutions of equations of two-dimensional hydrodynamics of an incompressible fluid”, TMF, 147:1 (2006), 64–72; Theoret. and Math. Phys., 147:1 (2006), 501–508

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This publication is cited in the following 9 articles:

Alexei Cheviakov, Peng Zhao, CMS/CAIMS Books in Mathematics, 10, Analytical Properties of Nonlinear Partial Differential Equations, 2024, 79
Oleg I. Morozov, “Extensions of the symmetry algebra and Lax representations for the two-dimensional Euler equation”, Journal of Geometry and Physics, 202 (2024), 105233
S. Artychev, “Generalization of the Landau submerged jet solution”, Theoret. and Math. Phys., 186:2 (2016), 148–155
S.G. Artyshev, “The description of several plane rotating flows of an incompressible fluid using cylindrical functions”, Journal of Applied Mathematics and Mechanics, 79:2 (2015), 159
Artyshev S.G., “Ob odnom klasse tochnykh reshenii uravnenii dvumernoi gidrodinamiki neszhimaemoi zhidkosti”, Vestnik natsionalnogo issledovatelskogo yadernogo universiteta MIFI, 2:1 (2013), 47–47
Yurova A.A., “Dinamika lokalizovannogo impulsa, opisyvaemogo uravneniem Devi–Styuartsona II”, Vestnik Baltiiskogo federalnogo universiteta im. I. Kanta, 2011, no. 5, 12–17
Hu Xiao-Rui, Chen Yong, Huang Fei, “Symmetry analysis and explicit solutions of the (3+1)-dimensional baroclinic potential vorticity equation”, Chinese Physics B, 19:8 (2010), 080203
Lou S.Y., Jia M., Huang F., Tang X.Y., “Backlund transformations, solitary waves, conoid waves and Bessel waves of the (2+1)-dimensional Euler equation”, Internat. J. Theoret. Phys., 46:8 (2007), 2082–2095
Lou S.Y., Jia M., Tang X.Y., Huang F., “Vortices, circumfluence, symmetry groups, and Darboux transformations of the (2+1)-dimensional Euler equation”, Phys. Rev. E (3), 75:5 (2007), 056318, 11 pp.

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

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