The Free Boundary of Steady Axisymmetric Inviscid Flow with Vorticity I: Near the Degenerate Point

In this paper, we investigate the singularity near the degenerate points of the steady axisymmetric flow with general vorticity of an inviscid incompressible fluid acted on by gravity and with a free surface. We called the points on the free boundary at which the gradient of the stream function vani...

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Bibliographic Details
Published in:Communications in mathematical physics 2023-06, Vol.400 (3), p.2137-2179
Main Authors: Du, Lili, Huang, Jinli, Pu, Yang
Format: Article
Language:English
Subjects:
Axisymmetric flow
Classical and Quantum Gravitation
Complex Systems
Cusps
Flatness
Fluid flow
Free boundaries
Free surfaces
Incompressible flow
Incompressible fluids
Inviscid flow
Mathematical and Computational Physics
Mathematical Physics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Singularities
Stream functions (fluids)
Theoretical
Vorticity
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Summary:In this paper, we investigate the singularity near the degenerate points of the steady axisymmetric flow with general vorticity of an inviscid incompressible fluid acted on by gravity and with a free surface. We called the points on the free boundary at which the gradient of the stream function vanishes as the degenerate points. The main results in this paper give the different classifications of the singularity near the degenerate points on the free surface. More precisely, we obtained that at the stagnation points, the possible profiles must be a Stokes corner, a horizontal cusp, or a horizontal flatness. At the degenerate points on the symmetric axis except the origin, the wave profile must be a cusp. At the origin, the possible wave profiles must be a Garabedian pointed bubble, a horizontal cusp, or a horizontal flatness.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-023-04651-7