Geodesic
One method for constructing exact solutions of equations of two-dimensional hydrodynamics of an incompressible fluid
Teoretičeskaâ i matematičeskaâ fizika, Tome 147 (2006) no. 1, pp. 64-72 Cet article a éte moissonné depuis la source Math-Net.Ru

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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
Mots-clés : exact solutions. 
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A. V. Yurov; A. A. Yurova. One method for constructing exact solutions of equations of two-dimensional hydrodynamics of an incompressible fluid. Teoretičeskaâ i matematičeskaâ fizika, Tome 147 (2006) no. 1, pp. 64-72. http://geodesic.mathdoc.fr/item/TMF_2006_147_1_a4/

[1] T. Kato, Proc. Symp. Pure Math. Part 2, 45 (1986), 1 | MR | Zbl

[2] T. Kato, J. Funct. Anal., 9 (1972), 296 ; “Quasi-linear equations of evolution with applications to partial differential equations”, Spectral Theory and Differential Equations, Proc. of Symp. (Dundee, Scotland, July 1–9, 1974), Lect. Notes Math., 448, ed. W. N. Everitt, Springer, Berlin, 1975, 25 | DOI | MR | Zbl | DOI | MR

[3] P. Constantin, J. Wu, Indiana Univ. Math. J., 45:1 (1996), 67 ; J. Wu, J. Diff. Equat., 142:2 (1998), 413 | DOI | MR | Zbl | DOI | MR

[4] V. I. Arnold, Ann. Inst. Fourier, 16:1 (1966), 319 | DOI | MR | Zbl

[5] J. E. Marsden, Lectures on Mechanics, Lond. Math. Soc. Lect. Note Ser., 174, Camb. Univ. Press, Cambridge, 1992 | MR | Zbl

[6] S. Friedlander, M. Vishik, Phys. Lett. A, 148:6–7 (1990), 313 ; Nonlinearity, 6:2 (1993), 231 | DOI | MR | Zbl | DOI | MR | Zbl

[7] Y. Li, A. Yurov, Stud. Appl. Math., 111 (2003), 101 | DOI | MR | Zbl

[8] L. D. Landau, E. M. Lifshits, Gidrodinamika, Nauka, M., 1986 | MR

[9] A. R. Its, A. V. Rybin, M. A. Sall, TMF, 74:1 (1988), 29 | MR | Zbl