Remarks on Stationary and Uniformly-rotating Vortex Sheets: Rigidity Results
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AbstractIn this paper, we show that the only solution of the vortex sheet equation, either stationary or uniformly rotating with negative angular velocity $$\Omega $$ Ω , 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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1980 ◽
Vol 373
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pp. 67-91
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1992 ◽
Vol 112
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pp. 527-534
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1967 ◽
Vol 30
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pp. 177-196
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1999 ◽
Vol 378
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pp. 233-267
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