Nonlinear stability for stationary helical vortices

Benvenutti, Maicon J.

doi:10.1007/s00030-020-0620-4

Cited by 4 publications

(2 citation statements)

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“…[10] considered travelling-rotating invariant Euler flows with helical symmetry concentrating near a single helical filament in the whole space R 3 . As for the steady solution of 3D Euler equations with helical symmetry, nonlinear stability for stationary smooth Euler flows with helical symmetry is considered in [2] by using the direct method of Lyapunov. More results of the existence and regularity of Euler equation with helical symmetry can be found in [1,4,12,19] for instance.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

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Desingularization of 3D steady Euler equation with helical symmetry

Cao¹,

Wu²

2022

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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 streamfunction 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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