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

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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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Communications in Mathematical Physics, 2021, vol. 386, p. 1845-1879

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cc by (c) Gómez Serrano, Javier et al., 2021

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Articles publicats en revistes (Matemàtiques i Informàtica)

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