Some solutions of the Euler system of an inviscid incompressible fluid

Oleg V. Kaptsov

Institute of computational modelling SB RAS, Krasnoyarsk, Russian Federation

Abstract: 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: Euler equations, group of point transformations, invariant solutions, vortices, jets.

UDC: 532.5+517.9

Received: 10.04.2022
Received in revised form: 02.06.2022
Accepted: 08.08.2022

Language: English

DOI: 10.17516/1997-1397-2022-15-5-672-678

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