71 citations · 267 across the 38 of their papers we have counts for
35 papers · 1 filter
The good commutator approach to global asymptotics for the Schrödinger equation with variable coefficients
Sung-Jin Oh, Federico Pasqualotto, Ning Tang
We present a robust physical-space approach to establish time decay and global asymptotics of solutions to variable-coefficient Schrödinger equations in -dimensions. As an i…
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…
Initial data gluing in the asymptotically flat regime via solution operators with prescribed support properties
Yuchen Mao, Sung-Jin Oh, Zhongkai Tao
We give new proofs of general relativistic initial data gluing results on unit-scale annuli based on explicit solution operators for the linearized constraint equation around the f…
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 in any sufficiently regular Sobolev spaces, w…
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…
Stability of the Catenoid for the Hyperbolic Vanishing Mean Curvature Equation Outside Symmetry
Jonas Luhrmann, Sung-Jin Oh, Sohrab Shahshahani
We study the problem of stability of the catenoid, which is an asymptotically flat rotationally symmetric minimal surface in Euclidean space, viewed as a stationary solution to the…
Soliton resolution for equivariant self-dual Chern-Simons-Schrödinger equation in weighted Sobolev class
Kihyun Kim, Soonsik Kwon, Sung-Jin Oh
We consider the self-dual Chern-Simons-Schrödinger equation (CSS) under equivariant symmetry, which is a -critical equation. It is known that (CSS) admits solitons and finit…
Gradient blow-up for dispersive and dissipative perturbations of the Burgers equation
Sung-Jin Oh, Federico Pasqualotto
We consider a class of dispersive and dissipative perturbations of the inviscid Burgers equation, which includes the fractional KdV equation of order , and the fractal Burgers e…
Blow-up dynamics for smooth finite energy radial data solutions to the self-dual Chern-Simons-Schrödinger equation
Kihyun Kim, Soonsik Kwon, Sung-Jin Oh
We consider the finite-time blow-up dynamics of solutions to the self-dual Chern-Simons-Schrödinger (CSS) equation (also referred to as the Jackiw-Pi model) near the radial soliton…
Asymptotic Stability of Harmonic Maps on the Hyperbolic Plane Under the Schrödinger Maps Evolution
Andrew Lawrie, Jonas Lührmann, Sung-Jin Oh +1
We consider the Cauchy problem for the Schrödinger maps evolution when the domain is the hyperbolic plane. An interesting feature of this problem compared to the more widely studie…
On the Cauchy problem for the Hall and electron magnetohydrodynamic equations without resistivity I: illposedness near degenerate stationary solutions
In-Jee Jeong, Sung-Jin Oh
In this article, we prove various illposedness results for the Cauchy problem for the incompressible Hall- and electron-magnetohydrodynamic (MHD) equations without resistivity. The…
Local smoothing estimates for Schrödinger equations on hyperbolic space
Andrew Lawrie, Jonas Luhrmann, Sung-Jin Oh +1
We establish global-in-time frequency localized local smoothing estimates for Schrödinger equations on hyperbolic space . In the presence of symmetric first and zerot…
The Threshold Theorem for the -dimensional Yang--Mills equation: an overview of the proof
Sung-Jin Oh, Daniel Tataru
This article is devoted to the energy critical hyperbolic Yang--Mills system in the dimensional Minkowski space, which is considered by the authors in a sequence of four pa…
The hyperbolic Yang--Mills equation in the caloric gauge. Local well-posedness and control of energy dispersed solutions
Sung-Jin Oh, Daniel Tataru
This is the second part in a four-paper sequence, which establishes the Threshold Conjecture and the Soliton Bubbling vs.~Scattering Dichotomy for the hyperbolic Yang--Mills equati…
The threshold conjecture for the energy critical hyperbolic Yang--Mills equation
Sung-Jin Oh, Daniel Tataru
This article represents the fourth and final part of a four-paper sequence whose aim is to prove the Threshold Conjecture as well as the more general Dichotomy Theorem for the ener…
The hyperbolic Yang--Mills equation for connections in an arbitrary topological class
Sung-Jin Oh, Daniel Tataru
This is the third part of a four-paper sequence, which establishes the Threshold Conjecture and the Soliton-Bubbling vs.~Scattering Dichotomy for the energy critical hyperbolic Yan…
The Yang--Mills heat flow and the caloric gauge
Sung-Jin Oh, Daniel Tataru
This is the first part of the four-paper sequence, which establishes the Threshold Conjecture and the Soliton Bubbling vs.~Scattering Dichotomy for the energy critical hyperbolic Y…
Global well-posedness of high dimensional Maxwell-Dirac for small critical data
Cristian Gavrus, Sung-Jin Oh
In this paper, we prove global well-posedness of the massless Maxwell-Dirac equation in Coulomb gauge on for data with small scale-critical Sobolev…
Small data global existence and decay for relativistic Chern-Simons equations
Myeongju Chae, Sung-Jin Oh
We establish a general small data global existence and decay theorem for Chern-Simons theories with a general gauge group, coupled with a massive relativistic field of spin 0 or 1/…
The Cauchy problem for wave maps on hyperbolic space in dimensions
Andrew Lawrie, Sung-Jin Oh, Sohrab Shahshahani
We establish global well-posedness and scattering for wave maps from -dimensional hyperbolic space into Riemannian manifolds of bounded geometry for initial data that is small i…
Equivariant Wave Maps on the Hyperbolic Plane with Large Energy
Andrew Lawrie, Sung-Jin Oh, Sohrab Shahshahani
In this paper we continue the analysis of equivariant wave maps from 2-dimensional hyperbolic space into surfaces of revolution that was initiated in [13, 14]. When the target is t…
Global well-posedness and scattering of the (4+1)-dimensional Maxwell-Klein-Gordon equation
Sung-Jin Oh, Daniel Tataru
This article constitutes the final and main part of a three-paper sequence, whose goal is to prove global well-posedness and scattering of the energy critical Maxwell-Klein-Gordon…
Energy dispersed solutions for the (4+1)-dimensional Maxwell-Klein-Gordon equation
Sung-Jin Oh, Daniel Tataru
This article is devoted to the mass-less energy critical Maxwell-Klein-Gordon system in 4+1 dimensions. In earlier work of the second author, joint with Krieger and Sterbenz, we ha…
Local well-posedness of the (4+1)-dimensional Maxwell-Klein-Gordon equation at energy regularity
Sung-Jin Oh, Daniel Tataru
This paper is the first part of a trilogy dedicated to a proof of global well-posedness and scattering of the (4+1)-dimensional mass-less Maxwell-Klein-Gordon equation (MKG) for an…