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. 2022 Jun 27;380(2226):20210045.
doi: 10.1098/rsta.2021.0045. Epub 2022 May 9.

Remarks on stationary and uniformly rotating vortex sheets: flexibility results

Javier Gómez-Serrano  1   2   3 , Jaemin Park  2 , Jia Shi  4 , Yao Yao  5
Affiliations

Remarks on stationary and uniformly rotating vortex sheets: flexibility results

Javier Gómez-Serrano et al. Philos Trans A Math Phys Eng Sci. .

Abstract

In this paper, we construct new, uniformly rotating solutions of the vortex sheet equation bifurcating from circles with constant vorticity amplitude. The proof is accomplished via a Lyapunov-Schmidt reduction and a second-order expansion of the reduced system. This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 2)'.

Keywords: Lyapunov–Schmidt; bifurcation; incompressible; uniformly rotating; vortex sheet.

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