7 citations · 18 across the 10 of their papers we have counts for
10 papers
Exponential ergodicity for the stochastic hyperbolic sine-Gordon equation on the circle
Kihoon Seong
In this paper, we show that the Gibbs measure of the stochastic hyperbolic sine-Gordon equation on the circle is the unique invariant measure for the Markov process. Moreover, the…
Phase transition of singular Gibbs measures for three-dimensional Schrödinger-wave system
Kihoon Seong
We study singular Gibbs measures for the three-dimensional Schrödinger-wave system, also known as the Yukawa system. Our primary result is the phase transition between weak and str…
Lecture notes on tree-free regularity structures
Felix Otto, Kihoon Seong, Markus Tempelmayr
These lecture notes are intended as reader's digest of recent work on a diagram-free approach to the renormalized centered model in Hairer's regularity structures. More precisely,…
Focusing Gibbs measures with harmonic potential
Tristan Robert, Kihoon Seong, Leonardo Tolomeo +1
In this paper, we study the Gibbs measures associated to the focusing nonlinear Schrödinger equation with harmonic potential on Euclidean spaces. We establish a dichotomy for norma…
Invariant Gibbs dynamics for the two-dimensional Zakharov-Yukawa system
Kihoon Seong
We study the Gibbs dynamics for the Zakharov-Yukawa system on the two-dimensional torus , namely a Schrödinger-wave system with a Zakharov-type coupling . We…
Transport of Gaussian measures under the flow of one-dimensional fractional nonlinear Schrödinger equations
Justin Forlano, Kihoon Seong
We study the transport property of Gaussian measures on Sobolev spaces of periodic functions under the dynamics of the one-dimensional cubic fractional nonlinear Schrödinger equati…
Quasi-invariant Gaussian measures for the cubic fourth order nonlinear Schrödinger equation in negative Sobolev spaces
Tadahiro Oh, Kihoon Seong
We continue the study on the transport properties of the Gaussian measures on Sobolev spaces under the dynamics of the cubic fourth order nonlinear Schrödinger equation. By conside…
A remark on Gibbs measures with log-correlated Gaussian fields
Tadahiro Oh, Kihoon Seong, Leonardo Tolomeo
We study Gibbs measures with log-correlated base Gaussian fields on the -dimensional torus. In the defocusing case, the construction of such Gibbs measures follows from Nelson's…
Low regularity a priori estimates for the fourth order cubic nonlinear Schrödinger equation
Kihoon Seong
We consider the low regularity behavior of the fourth order cubic nonlinear Schrödinger equation (4NLS) \begin{align*} \begin{cases} i\partial_tu+\partial_x^4u=\pm \vert u \vert^2u…
Well-Posedness and Ill-Posedness for the Fourth order cubic nonlinear Schrödinger equation in negative Sobolev spaces
Kihoon Seong
We consider the Cauchy problem for the fourth order cubic nonlinear Schrödinger equation (4NLS). The main goal of this paper is to prove low regularity well-posedness and mild ill-…