Solutions of the Euler equations and stationary structures in an inviscid fluid

O.V. Kaptsov

17-Mar-2022, 11:00-12:00 (2 years ago)

Abstract: The Euler equations describing two-dimensional steady flows of an inviscid fluid are studied. These equations are reduced to one equation for the stream function and then, using the Hirota function, solutions of three nonlinear elliptic equations are found. The solutions found are interpreted as sources in a rotating fluid, jets, chains of sources and sinks, vortex structures. We propose a new simple method for constructing solutions in the form of rational expressions of elliptic functions. It is shown that the flux of fluid across a closed curve is quantized in the case of the elliptic Sin-Gordon equation.

mathematical physicsanalysis of PDEsclassical analysis and ODEsdynamical systemsnumerical analysisexactly solvable and integrable systemsfluid dynamics

Audience: researchers in the topic


Mathematical models and integration methods

Organizers: Oleg Kaptsov, Sergey P. Tsarev*, Yury Shan'ko*
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