In-Jee Jeong

activity

20242026

collaborators

10 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

Global dynamics of a single vortex ring

Dengjun Guo, In-Jee Jeong, Lifeng Zhao

We study the global-in-time dynamics of vortex rings for the three-dimensional incompressible Euler equations, under the assumption of axisymmetric flows without swirl. For a broad…

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

Instantaneous continuous loss of Sobolev regularity for the 3D incompressible Euler equation

In-Jee Jeong, Luis Martínez-Zoroa, Wojciech S. Ożański

We prove instantaneous and continuous-in-time loss of supercritical Sobolev regularity for the 3D incompressible Euler equations in $R^{3}$ . Namely, for any $s \in (0, 3/2)$ …

math.AP2025

Superlinear gradient growth for 2D Euler equation without boundary

In-Jee Jeong, Yao Yao, Tao Zhou

We consider the vorticity gradient growth of solutions to the two-dimensional Euler equations in domains without boundary, namely in the torus $T^{2}$ and the whole plane…

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.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-…