6 papers
Support growth of vorticity for bi-rotational Euler flows in high dimensions
In-Jee Jeong, Deokwoo Lim
We study incompressible Euler equations in with under bi-rotational symmetry without swirl, which reduces the Euler equations to a scalar vorticity advecti…
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…
On the optimal rate of vortex stretching for axisymmetric Euler flows without swirl
Deokwoo Lim, In-Jee Jeong
For axisymmetric flows without swirl and compactly supported initial vorticity, we prove the upper bound of for the growth of the vorticity maximum, which was conjectured…
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…