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

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.

34 pages

References in corpus (3)

• Desingularization of vortices for the Euler equation
• Regularization of point vortices for the Euler equation in dimension two
• Regularization of point vortices for the Euler equation in dimension two, part II

Cited by in corpus (7)

• Vortex motion for the lake equations
• Vanishing viscosity limit for axisymmetric vortex rings
• Steady Contiguous Vortex-Patch Dipole Solutions of the 2D Incompressible Euler Equation
• Uniqueness and stability of steady vortex rings for 3D incompressible Euler equation
• Rigidity of Beltrami fields with a non-constant proportionality factor
• Existence of vortex rings in Beltrami flows
• Multiple Vortices for the Shallow Water Equation