Asymptotic estimates for concentrated vortex pairs

Abstract

Burton-Lopes Filho-Nussenzveig Lopes (2013) [6] studied the existence and stability of slowly traveling vortex pairs as maximizers of the kinetic energy penalized by the impulse relative to a prescribed rearrangement class. In this paper, we prove that after a suitable scaling transformation the maximization problem studied by Burton-Lopes Filho-Nussenzveig Lopes in fact gives rise to a family of stable concentrated vortex pairs approaching a pair of point vortices with equal magnitude and opposite signs. The key ingredient of the proof is to deduce a uniform bound for the size of the supports of the scaled maximizers.