In-Jee Jeong

activity

20142026

most citedFinite-time Singularity Formation for Strong Solutions to the Boussinesq System

26 citations · 156 across the 50 of their papers we have counts for

collaborators

50 papers

math.AP2026

Global well-posedness for the incompressible Euler equations in an endpoint Sobolev space

Raphaël Danchin, In-Jee Jeong

We consider the initial value problem for the vorticity equation in the endpoint critical Sobolev space $W^{d, 1} (R^{d})$ for $d = 2, 3$ . In two dimensions, we prove global…

math.AP2023

Weakened vortex stretching effect in three scale hierarchy for the 3D Euler equations

In-Jee Jeong, Jungkyoung Na, Tsuyoshi Yoneda

We consider the 3D incompressible Euler equations under the following three scale hierarchical situation: large-scale vortex stretching the middle-scale, and at the same time, the…

math.AP2023

Illposedness for dispersive equations: Degenerate dispersion and Takeuchi--Mizohata condition

In-Jee Jeong, Sung-Jin Oh

We provide a unified viewpoint on two illposedness mechanisms for dispersive equations in one spatial dimension, namely degenerate dispersion and (the failure of) the Takeuchi--Miz…

math.AP2023★ 2 cited

Illposedness via degenerate dispersion for generalized surface quasi-geostrophic equations with singular velocities

Dongho Chae, In-Jee Jeong, Sung-Jin Oh

We prove strong nonlinear illposedness results for the generalized SQG equation $\partial_{t} θ + \nabla^{⊥} Γ [θ] \cdot \nabla θ = 0$ in any sufficiently regular Sobolev spaces, w…

math.AP2023★ 1 cited

Well-posedness for Ohkitani model and long-time existence for surface quasi-geostrophic equations

Dongho Chae, In-Jee Jeong, Jungkyoung Na +1

We consider the Cauchy problem for the logarithmically singular surface quasi-geostrophic (SQG) equation, introduced by Ohkitani, $$\partial_t θ- \nabla^\perp \log(10+(-Δ)^{\frac12…

math.AP2023

On well-posedness of $α$ -SQG equations in the half-plane

In-Jee Jeong, Junha Kim, Yao Yao

We investigate the well-posedness of $α$ -SQG equations in the half-plane, where $α = 0$ and $α = 1$ correspond to the 2D Euler and SQG equations respectively. For $0 < α \leq 1/2$ , we prov…

math.AP2023★ 8 cited

Twisting in Hamiltonian Flows and Perfect Fluids

Theodore D. Drivas, Tarek M. Elgindi, In-Jee Jeong

We introduce a notion of stability for non-autonomous Hamiltonian flows on two-dimensional annular surfaces. This notion of stability is designed to capture the sustained twisting…

math.AP2023★ 1 cited

Logarithmic spirals in 2d perfect fluids

In-Jee Jeong, Ayman R. Said

We study logarithmic spiraling solutions to the 2d incompressible Euler equations which solve a nonlinear transport system on $S$ . We show that this system is locally well…

math.AP2022

Axi-symmetric solutions for active vector models generalizing 3D Euler and electron--MHD equations

Dongho Chae, Kyudong Choi, In-Jee Jeong

We study systems interpolating between the 3D incompressible Euler and electron--MHD equations, given by \begin{equation*} \partial_t B + V \cdot \nabla B = B\cdot \nabla V, \qquad…

math.AP2022

Global regularity for some axisymmetric Euler flows in $R^{d}$

Kyudong Choi, In-Jee Jeong, Deokwoo Lim

We consider axisymmetric Euler flows without swirl in $R^{d}$ with $d \geq 4$ , for which the global regularity of smooth solutions is an open problem. When $d = 4$ , we obta…

math.AP2022

Active vector models generalizing 3D Euler and electron--MHD equations

Dongho Chae, In-Jee Jeong

We introduce an active vector system, which generalizes both the 3D Euler equations and the electron--magnetohydrodynamic equations (E--MHD). We may as well view the system as sing…

math.AP2022

On evolution of corner-like gSQG patches

Junekey Jeon, In-Jee Jeong

We study the evolution of corner-like patch solutions to the generalized SQG equations. Depending on the angle size and order of the velocity kernel, the corner instantaneously ben…

math.AP2022

Stability and instability of Kelvin waves

Kyudong Choi, In-Jee Jeong

The $m$ -waves of Kelvin are uniformly rotating patch solutions of the 2D Euler equations with $m$ -fold rotational symmetry for $m \geq 2$ . For Kelvin waves sufficiently close to the…

math.AP2022★ 4 cited

Stability of monotone, non-negative, and compactly supported vorticities in the half cylinder and infinite perimeter growth for patches

Kyudong Choi, In-Jee Jeong, Deokwoo Lim

We consider the incompressible Euler equations in the half cylinder $R_{> 0} \times T$ . In this domain, any vorticity which is independent of $x_{2}$ defines a statio…

math.AP2022

Global-in-time existence of weak solutions for Vlasov-Manev-Fokker-Planck system

Young-Pil Choi, In-Jee Jeong

We consider the Vlasov-Manev-Fokker-Planck (VMFP) system in three dimensions, which differs from the Vlasov-Poisson-Fokker-Planck in that it has the gravitational potential of the…

math.AP2022

Well-posedness and singularity formation for Vlasov--Riesz system

Young-Pil Choi, In-Jee Jeong

We investigate the Cauchy problem for the Vlasov--Riesz system, which is a Vlasov equation featuring an interaction potential generalizing previously studied cases, including the C…

math.AP2021★ 3 cited

On vortex stretching for anti-parallel axisymmetric flows

Kyudong Choi, In-Jee Jeong

We consider axisymmetric incompressible inviscid flows without swirl in $R^{3}$ , under the assumption that the axial vorticity is non-positive in the upper half space and od…

math.AP2021★ 1 cited

A simple proof of ill-posedness for incompressible Euler equations in critical Sobolev spaces

In-Jee Jeong, Junha Kim

We provide a simple proof that the Cauchy problem for the incompressible Euler equations in $R^{d}$ with any $d \geq 3$ is ill-posed in critical Sobolev spaces, extending an…

math.AP2021★ 1 cited

Loss of regularity for the 2D Euler equations

In-Jee Jeong

In this note, we construct solutions to the 2D Euler equations which belong to the Yudovich class but lose $W^{1, p}$ regularity continuously with time.

math.AP2021

Infinite growth in vorticity gradient of compactly supported planar vorticity near Lamb dipole

Kyudong Choi, In-Jee Jeong

We prove linear in time filamentation for perturbations of the Lamb dipole, which is a traveling wave solution to the incompressible Euler equations in $R^{2}$ . The main ing…

math.AP2021★ 16 cited

Strong illposedness for SQG in critical Sobolev spaces

In-Jee Jeong, Junha Kim

We prove that the inviscid surface quasi-geostrophic (SQG) equations are strongly ill-posed in critical Sobolev spaces: there exists an initial data $H^{2}(\bbT^2)$ without any sol…

math.AP2021★ 1 cited

Filamentation near Hill's vortex

Kyudong Choi, In-Jee Jeong

For the axisymmetric incompressible Euler equations, we prove linear in time filamentation near Hill's vortex: there exists an arbitrary small outward perturbation growing linearly…

math.AP2021

Preservation of log-Hölder coefficients of the vorticity in the transport equation

Dongho Chae, In-Jee Jeong

We show that the log-Hölder coefficients of a solution to the transport equation is preserved in time.

math.AP2021★ 17 cited

Well-posedness and singularity formation for inviscid Keller-Segel-fluid system of consumption type

In-Jee Jeong, Kyungkeun Kang

We consider the Keller-Segel system of consumption type coupled with an incompressible fluid equation. The system describes the dynamics of oxygen and bacteria densities evolving w…

Global well-posedness for the incompressible Euler equations in an endpoint Sobolev space

Weakened vortex stretching effect in three scale hierarchy for the 3D Euler equations

Illposedness for dispersive equations: Degenerate dispersion and Takeuchi--Mizohata condition

Illposedness via degenerate dispersion for generalized surface quasi-geostrophic equations with singular velocities

Well-posedness for Ohkitani model and long-time existence for surface quasi-geostrophic equations

On well-posedness of α-SQG equations in the half-plane

Twisting in Hamiltonian Flows and Perfect Fluids

Logarithmic spirals in 2d perfect fluids

Axi-symmetric solutions for active vector models generalizing 3D Euler and electron--MHD equations

Global regularity for some axisymmetric Euler flows in Rd

Active vector models generalizing 3D Euler and electron--MHD equations

On evolution of corner-like gSQG patches

Stability and instability of Kelvin waves

Stability of monotone, non-negative, and compactly supported vorticities in the half cylinder and infinite perimeter growth for patches

Global-in-time existence of weak solutions for Vlasov-Manev-Fokker-Planck system

Well-posedness and singularity formation for Vlasov--Riesz system

On vortex stretching for anti-parallel axisymmetric flows

A simple proof of ill-posedness for incompressible Euler equations in critical Sobolev spaces

Loss of regularity for the 2D Euler equations

Infinite growth in vorticity gradient of compactly supported planar vorticity near Lamb dipole

Strong illposedness for SQG in critical Sobolev spaces

Filamentation near Hill's vortex

Preservation of log-Hölder coefficients of the vorticity in the transport equation

Well-posedness and singularity formation for inviscid Keller-Segel-fluid system of consumption type

On well-posedness of $α$ -SQG equations in the half-plane

Global regularity for some axisymmetric Euler flows in $R^{d}$