Ken Abe

activity

20242026

collaborators

11 papers

math.AP2026

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…

math.AP2026

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…

math.AP2026

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…

math.AP2026

Minus one Homogeneous Euler Flows are Geodesible

Ken Abe, Naoki Sato, Chunjing Xie

In this paper, we study $(- 1)$ -homogeneous steady solutions to the Euler equations on $R^{n} ∖ {0}$ . In low dimensions $n = 2, 3$ , such flows are known to be essentia…

math.AP2025

Homogeneous steady states for the generalized surface quasi-geostrophic equations

Ken Abe, Javier Gómez-Serrano, In-Jee Jeong

We consider homogeneous (stationary self-similar) solutions to the generalized surface quasi-geostrophic (gSQG) equations parametrized by the constant $0 < s < 1$ , representing the 2D…

math.AP2025

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 $R^{2}$ and question under which initial disturbance the Lam…

math.AP2025

Stability for multiple Lamb dipoles

Ken Abe, In-Jee Jeong, Yao Yao

In the class of nonnegative vorticities on the half-plane, we establish the Lyapunov stability of finite sums of Lamb dipoles under the initial assumptions that the dipoles are suf…

math.AP2025

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…

math.AP2025

MHS equilibria in the non-resistive limit to the randomly forced resistive magnetic relaxation equations

Ken Abe, In-Jee Jeong, Federico Pasqualotto +1

We consider randomly forced resistive magnetic relaxation equations (MRE) with resistivity $κ > 0$ and a force proportional to $κ$ on the flat $d$ -torus $T^{d}$ for $…

math-ph2025

Topological Invariants in Higher-Dimensional Magnetohydrodynamics

Naoki Sato, Ken Abe, Michio Yamada

It is well known that the three-dimensional ideal magnetohydrodynamics (MHD) equations possess three magnetic invariants: (M) magnetic helicity, (C) cross helicity, and (P) the mea…

math.AP2024

Stationary self-similar profiles for the two-dimensional inviscid Boussinesq equations

Ken Abe, Daniel Ginsberg, In-Jee Jeong

We consider ( $- α$ )-homogeneous solutions (stationary self-similar solutions of degree $- α$ ) to the two-dimensional inviscid Boussinesq equations in a half-plane. We show their non-…