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TMF, 2006, Volume 147, Number 1, Pages 64–72 (Mi tmf2023)  

This article is cited in 6 scientific papers (total in 6 papers)

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

A. V. Yurova, A. A. Yurovab

a Immanuel Kant State University of Russia
b Kaliningrad State University

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

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

Full text: PDF file (224 kB)
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English version:
Theoretical and Mathematical Physics, 2006, 147:1, 501–508

Bibliographic databases:

Received: 12.07.2005
Revised: 21.10.2005

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

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    2. 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.  crossref  mathscinet  adsnasa  isi  scopus  scopus
    3. 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  crossref  mathscinet  isi  scopus  scopus
    4. Yurova A.A., “Dinamika lokalizovannogo impulsa, opisyvaemogo uravneniem Devi–Styuartsona II”, Vestnik Baltiiskogo federalnogo universiteta im. I. Kanta, 2011, no. 5, 12–17  elib
    5. Artyshev S.G., “Ob odnom klasse tochnykh reshenii uravnenii dvumernoi gidrodinamiki neszhimaemoi zhidkosti”, Vestnik natsionalnogo issledovatelskogo yadernogo universiteta MIFI, 2:1 (2013), 47–47  elib
    6. S. Artychev, “Generalization of the Landau submerged jet solution”, Theoret. and Math. Phys., 186:2 (2016), 148–155  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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