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- W4298183768 abstract "A new important relation between fluid mechanics and differential geometry is established. We study smooth steady solutions to the Euler equations with the additional property: the velocity vector is orthogonal to the gradient of the pressure at any point. Such solutions are called Gavrilov flows. Local structure of a Gavrilov flow is described in terms of geometry of isobaric hypersurfaces. In the 3D case, we obtain a system of PDEs for an axisymmetric Gavrilov flow and find consistency conditions for the system. Two numerical examples of axisymmetric Gavrilov flows are presented: with pressure function periodic in the axial direction, and with isobaric surfaces diffeomorphic to the torus." @default.
- W4298183768 created "2022-10-01" @default.
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- W4298183768 date "2022-09-29" @default.
- W4298183768 modified "2023-09-23" @default.
- W4298183768 title "Steady flows of ideal incompressible fluid" @default.
- W4298183768 doi "https://doi.org/10.48550/arxiv.2209.14572" @default.
- W4298183768 hasPublicationYear "2022" @default.
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