Desingularization of 3D steady Euler equation with helical symmetry

Daomin Cao; Jie Wan

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arXiv · 2206.00196

Desingularization of 3D steady Euler equation with helical symmetry

Daomin Cao·Jie Wan

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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\to 0 $. Qualitative properties of those solutions are also discussed.

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Daomin Cao, Jie Wan. 2022-06-01. Desingularization of 3D steady Euler equation with helical symmetry. https://arxiv.org/abs/2206.00196

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