Desingularization of 3D steady Euler equation with helical symmetry

2022/06/01 by Cao, Daomin, Wan, Jie · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2206.00196

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 ε→ 0 . Qualitative properties of those solutions are also discussed.

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• Helical vortex filaments with compactly supported cross-sectional vorticity for the incompressible Euler equations in ℝ³

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