In-Jee Jeong - Publications

List of Publications by Topics

Singularities and Illposedness for hydrodynamic PDE

Stationary self-similar profiles for the two-dimensional inviscid Boussinesq equations (with Ken Abe and Dan Ginsberg)
Strong ill-posedness of SQG in critical Sobolev spaces (with Junha Kim)
A simple proof of ill-posedness for incompressible Euler equations in critical Sobolev spaces (with Junha Kim)
The incompressible Euler equations under octahedral symmetry: singularity formation in a fundamental domain (with Tarek Elgindi)
Loss of regularity for the 2D Euler equations
Finite-time Singularity Formation for Strong Solutions to the Boussinesq System (with Tarek Elgindi)
On the Effects of Advection and Vortex Stretching (with Tarek Elgindi)
Finite-time Singularity Formation for Strong Solutions to the axi-symmetric 3D Euler Equations (with Tarek Elgindi)
Ill-posedness for the incompressible Euler equations in critical Sobolev spaces (with Tarek Elgindi)
Discrete Schrödinger equation and ill-posedness for the Euler equation (with Benoit Pausader)

Stability issues for hydrodynamic PDE

Stability of vortex quadrupoles with odd-odd symmetry (with Kyudong Choi and Yao Yao)
On the optimal rate of vortex stretching for axisymmetric Euler flows without swirl (with Deokwoo Lim)
On existence of Sadovskii vortex patch: A touching pair of symmetric counter-rotating uniform vortex (with Kyudong Choi and Young-Jin Sim)
Twisting in Hamiltonian Flows and Perfect Fluids (with Tarek Elgindi and Theodore Drivas)
On vortex stretching for anti-parallel axisymmetric flows (with Kyudong Choi)
Filamentation near Hill's vortex (with Kyudong Choi)
Stability of monotone vorticities in the half cylinder and infinite perimeter growth for patches (with Kyudong Choi and Deokwoo Lim)
Stability and instability of Kelvin waves (with Kyudong Choi)
Infinite growth in vorticity gradient of compactly supported planar vorticity near Lamb dipole (with Kyudong Choi)
Growth of perimeter for vortex patches (with Kyudong Choi)
On Singular Vortex Patches, II: Long-time dynamics (with Tarek Elgindi)
Weakened vortex stretching effect in three scale hierarchy for the 3D Euler equations (with Jungkyoung Na and Tsuyoshi Yoneda)

Wellposedness for hydrodynamic PDE

Wellposedness of inviscid SQG in the half-plane (with Junha Kim and Hideyuki Miura)
On global regularity of some bi-rotational Euler flows (with Kyudong Choi and Deokwoo Lim)
On well-posedness of α-SQG equations in the half-plane (with Junha Kim and Yao Yao)
Logarithmic spirals in 2d perfect fluids (with Ayman Said)
Global regularity for some axisymmetric Euler flows in R^d (with Kyudong Choi and Deokwoo Lim)
Axi-symmetric solutions active vector models generalizing 3D Euler and electron–MHD equations (with Dongho Chae and Kyudong Choi)
On evolution of corner-like gSQG patches (with Junekey Jeon)
On Singular Vortex Patches, I: Well-posedness Issues (with Tarek Elgindi)
Active vector models generalizing 3D Euler and electron–MHD systems (with Dongho Chae)
Preservation of log-Hölder coefficients of the vorticity in the transport equation (with Dongho Chae)
Symmetries and Critical Phenomena in Fluids (with Tarek Elgindi)

MHD models and Quasilinear dispersive systems

MHS equilibria in the non-resistive limit to the randomly forced resistive magnetic relaxation equations (with Ken Abe, Federico Pasqualotto, and Naoki Sato)
On illposedness of the Hall and electron magnetohydrodynamic equations without resistivity on the whole space (with Sung-Jin Oh)
Wellposedness of the electron MHD without resistivity for large perturbations of the uniform magnetic field (with Sung-Jin Oh)
Illposedness for dispersive equations: Degenerate dispersion and Takeuchi--Mizohata condition (with Sung-Jin Oh)
Illposedness via degenerate dispersion for generalized surface quasi-geostrophic equations with singular velocities (with Dongho Chae and Sung-Jin Oh)
Well-posedness for Ohkitani model and long-time existence for surface quasi-geostrophic equations (with Dongho Chae, Jungkyoung Na and Sung-Jin Oh)
On the Cauchy problem for the Hall and electron magnetohydrodynamic equations without resistivity I: illposedness near degenerate stationary solutions (with Sung-Jin Oh)

Inviscid limit

Time periodic solutions to a heat equation with linear forcing and boundary conditions (with Sun-Chul Kim)
Anomalous Dissipation in Passive Scalar Transport (with Tarek Elgindi, Theodore Drivas, and Gautam Iyer)
Quasi-streamwise vortices and enhanced dissipation for the incompressible 3D Navier–Stokes equations (with Tsuyoshi Yoneda)
Vortex stretching and a modified zeroth law for the incompressible 3D Navier–Stokes equations (with Tsuyoshi Yoneda)
On stationary solutions and inviscid limits for generalized Constantin–Lax–Majda equation with O(1) forcing (with Sun-Chul Kim)
On the stationary solutions and inviscid limit for the generalized Proudman–Johnson equation with O(1)–forcing (with Sun-Chul Kim)
Enstrophy dissipation and vortex thinning for the incompressible 2D Navier–Stokes equations (with Tsuyoshi Yoneda)

Kinetic and related PDE

Well-posedness and singularity formation for Vlasov–Riesz system (with Young-Pil Choi)
Global weak solutions to Vlasov–Manev–Fokker–Planck system (with Young-Pil Choi)
On well-posedness and singularity formation for the Euler–Riesz system (with Young-Pil Choi)
Relaxation to fractional porous medium equation from Euler–Riesz system (with Young-Pil Choi)
Classical solutions to the fractional porous medium flow (with Young-Pil Choi)
Global Cauchy problem for the Vlasov--Riesz--Fokker--Planck system near the global Maxwellian (with Young-Pil Choi and Kyungkeun Kang)

Dyadic models in Fluid dynamics

Chemotaxis and mathematical biology

Well-posedness and singularity formation for inviscid Keller–Segel–fluid system of consumption type (with Kyungkeun Kang)

Random matrix theory

A Limit theorem for stochastically decaying partitions at the edge (with Sasha Sodin)

Dynamical Systems

Combinatorics

Gale–Robinson sequences and brane tilings (with Gregg Musiker and Sicong Zhang)