Geodesic
Some solutions of the Euler system of an inviscid incompressible fluid
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 15 (2022) no. 5, pp. 672-678

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We consider a system of two-dimensional Euler equations describing the motions of an inviscid incompressible fluid. It reduces to one non-linear equation with partial derivatives of the third order. A group of point transformations allowed by this equation is found. Some invariant solutions and solutions not related to invariance are constructed. The solutions found describe vortices, jet streams, and vortex-like formations.
Keywords: vortices
Mots-clés : Euler equations, group of point transformations, invariant solutions, jets. 
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     title = {Some solutions of the {Euler} system of an inviscid incompressible fluid},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
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Oleg V. Kaptsov. Some solutions of the Euler system of an inviscid incompressible fluid. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 15 (2022) no. 5, pp. 672-678. http://geodesic.mathdoc.fr/item/JSFU_2022_15_5_a14/