Desingularization of vortex rings and shallow water vortices by a semilinear elliptic problem

de Valeriola, Sébastien;Van Schaftingen, Jean
(2013) Archive for Rational Mechanics and Analysis — Vol. 210, n° 2, p. 409-450 (2013)

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Abstract
Steady vortices for the three-dimensional Euler equation for inviscid incompressible flows and for the shallow water equation are constructed and showed to tend asymptotically to singular vortex filaments. The construction is based on the asymptotic study of solutions to a semilinear elliptic problem.
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de Valeriola, S., & Van Schaftingen, J. (2013). Desingularization of vortex rings and shallow water vortices by a semilinear elliptic problem. Archive for Rational Mechanics and Analysis, 210(2), 409-450. https://doi.org/10.1007/s00205-013-0647-3 (Original work published 2013)