5 papers
Existence and stability of Sadovskii vortices: from patch to smooth vortices
Ken Abe, Kyudong Choi, In-Jee Jeong +2
We establish a scaling-invariant variational framework for steadily translating dipoles of the two-dimensional incompressible Euler equations. Specifically, we consider the maximiz…
Vortex atmospheres of traveling vortices: rigorous definition, existence, and topological classification
Kyudong Choi, In-Jee Jeong, Young-Jin Sim
In incompressible and inviscid fluids, the vortex atmosphere refers to the collection of fluid particles outside the support of a traveling vortex that are nevertheless carried alo…
Stability of Lamb dipoles for odd-symmetric and non-negative initial disturbances without the finite mass condition
Ken Abe, Kyudong Choi, In-Jee Jeong
In this paper, we consider the stability of the Lamb dipole solution of the two-dimensional Euler equations in and question under which initial disturbance the Lam…
On existence of Sadovskii vortex patch: A touching pair of symmetric counter-rotating uniform vortex
Kyudong Choi, In-Jee Jeong, Young-Jin Sim
The Sadovskii vortex patch is a traveling wave for the two-dimensional incompressible Euler equations consisting of an odd symmetric pair of vortex patches touching the symmetry ax…
Stability of vortex quadrupoles with odd-odd symmetry
Kyudong Choi, In-Jee Jeong, Yao Yao
For the 2D incompressible Euler equations, we establish global-in-time () stability of vortex quadrupoles satisfying odd symmetry with respect to both axes. Speci…