Desingularization of vortex rings and shallow water vortices by   semilinear elliptic problem
  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. 
S\'ebastien de Valeriola and Jean Van Schaftingen
math.AP