4 papers · 1 filter
Lamb dipole stability without sign condition
Ken Abe, Kyudong Choi, In-Jee Jeong +1
For the 2D incompressible Euler equations on the half-plane, we establish Lyapunov stability of the Lamb dipole without sign condition on the vorticity. The main challenge arises f…
A Variational Family of Traveling Vortex Dipoles: Transition, Uniqueness, and Stability
Ken Abe, In-Jee Jeong, Guolin Qin +1
We provide a unified description of a stable variational family of traveling vortex dipoles for the two-dimensional incompressible Euler equations, connecting the classical Lamb di…
Admissible Invariant-Torus Foliations for Steady Euler Flows
Naoki Sato, Ken Abe
In 1965, V. I. Arnold established a structure theorem guaranteeing the existence of a foliation by invariant surfaces for general three-dimensional steady Euler flows with non-cons…
Minus one Homogeneous Euler Flows are Geodesible
Ken Abe, Naoki Sato, Chunjing Xie
In this paper, we study -homogeneous steady solutions to the Euler equations on . In low dimensions , such flows are known to be essentia…