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Desingularization of 3D steady Euler equation with helical symmetry | | Daomin Cao
; Jie Wan
; | | Date: |
1 Jun 2022 | | Abstract: | In this paper, we study desingularization of steady solutions of 3D
incompressible Euler equation with helical symmetry in a general helical
domain. We construct a family of steady Euler flows with helical symmetry, such
that the associated vorticities tend asymptotically to a helical vortex
filament. The solutions are obtained by solving a semilinear elliptic problem
in divergence form with a parameter. By using the stream-function method, we
show the existence and asymptotic behavior of ground state solutions
concentrating near a single point as the parameter $ varepsilon o 0 $.
Qualitative properties of those solutions are also discussed. | | Source: | arXiv, 2206.00196 | | Services: | Forum | Review | PDF | Favorites | |
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