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arXiv · 2012.04548

Remarks on stationary and uniformly-rotating vortex sheets: Rigidity results

Javier Gómez-Serrano·Jaemin Park·Jia Shi·Yao Yao
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Abstract

In this paper, we show that the only solution of the vortex sheet equation, either stationary or uniformly rotating with negative angular velocity $\Omega$, such that it has positive vorticity and is concentrated in a finite disjoint union of smooth curves with finite length is the trivial one: constant vorticity amplitude supported on a union of nested, concentric circles. The proof follows a desingularization argument and a calculus of variations flavor.

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Javier Gómez-Serrano, Jaemin Park, Jia Shi, Yao Yao. 2020-12-08. Remarks on stationary and uniformly-rotating vortex sheets: Rigidity results. https://doi.org/10.1007/s00220-021-04146-3

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