On concentrated traveling vortex pairs with prescribed impulse

Wang, Guodong

doi:10.1090/tran/9105

On concentrated traveling vortex pairs with prescribed impulse
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by Guodong Wang;

Trans. Amer. Math. Soc. 377 (2024), 2635-2661

DOI: https://doi.org/10.1090/tran/9105

Published electronically: February 8, 2024

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Abstract:

In this paper, we consider a constrained maximization problem related to planar vortex pairs with prescribed impulse. We prove existence, stability and asymptotic behavior for the maximizers, hence obtain a family of stable traveling vortex pairs approaching a pair of point vortices with equal magnitude and opposite signs. As a corollary, we get fine asymptotic estimates for Burton’s vortex pairs with large impulse. We also consider a special non-concentrated case and prove a form of stability for the Chaplygin-Lamb dipole.

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