35 citations · 83 across the 30 of their papers we have counts for
31 papers
On steady states for the Vlasov-Schrödinger-Poisson system
Younghun Hong, Sangdon Jin
The Vlasov-Schrödinger-Poisson system is a kinetic-quantum hybrid model describing quasi-lower dimensional electron gases. For this system, we construct a large class of 2D kinetic…
On the NLS approximation for the nonlinear Klein-Gordon equation
Seokchang Hong, Younghun Hong
In this paper, developing a new approach based on Fourier analysis methods for dispersive PDEs, we establish a low regularity NLS approximation for the one-dimensional cubic Klein-…
On the nonlinear Schrödinger equation with a toroidal trap in the strong confinement regime
Younghun Hong, Sangdon Jin
We consider the 3D cubic nonlinear Schrödinger equation (NLS) with a strong toroidal trap. In the first part, we show that as the confinement is strengthened, a large class of glob…
Uniqueness and orbital stability of standing waves for the nonlinear Schrodinger equation with a partial confinement
Sangdon Jin, Younghun Hong
We consider the 3d cubic nonlinear Schrödinger equation (NLS) with a strong 2d harmonic potential. The model is physically relevant to observe the lower-dimensional dynamics of the…
Orbital stability for the mass-critical and supercritical pseudo-relativistic nonlinear Schrodinger equation
Sangdon Jin, Younghun Hong
For the one-dimensional mass-critical/supercritical pseudo-relativistic nonlinear Schrodinger equation, a stationary solution can be constructed as an energy minimizer under an add…
Strichartz estimates for higher-order Schrödinger equations and their applications
Younghun Hong, Chulkwang Kwak, Changhun Yang
In this paper, we consider the higher-order linear Schrödinger equations, that is, a formal finite Taylor expansion of the linear pseudo-relativistic equation. We establish the glo…
On the continuum limit for the discrete Nonlinear Schrödinger equation on a large finite cubic lattice
Younghun Hong, Chulkwang Kwak, Changhun Yang
In this study, we consider the nonlinear Schödinger equation (NLS) with the zero-boundary condition on a two- or three-dimensional large finite cubic lattice. We prove that its sol…
Korteweg--de Vries limit for the Fermi--Pasta--Ulam system
Younghun Hong, Chulkwang Kwak, Changhun Yang
In this paper, we develop dispersive PDE techniques for the Fermi--Pasta--Ulam (FPU) system with infinitely many oscillators, and we show that general solutions to the infinite FPU…
Semi-classical limit of quantum free energy minimizers for the gravitational Hartree equation
Woocheol Choi, Younghun Hong, Jinmyoung Seok
For the gravitational Vlasov-Poisson equation, Guo and Rein constructed a class of classical isotropic states as minimizers of free energies (or energy-Casimir functionals) under m…
Finite difference scheme for two-dimensional periodic nonlinear Schrödinger equations
Younghun Hong, Chulkwang Kwak, Shohei Nakamura +1
A nonlinear Schrödinger equation (NLS) on a periodic box can be discretized as a discrete nonlinear Schrödinger equation (DNLS) on a periodic cubic lattice, which is a system of fi…
Convergence rate of the finite element approximation for extremizers of Sobolev inequalities
Woocheol Choi, Younghun Hong, Jinmyoung Seok
In this paper, we are concerned with the convergence rate of a FEM based numerical scheme approximating extremal functions of the Sobolev inequality. We prove that when the domain…
Strong Convergence for Discrete Nonlinear Schrödinger equations in the Continuum Limit
Younghun Hong, Changhun Yang
We consider discrete nonlinear Schrödinger equations (DNLS) on the lattice whose linear part is determined by the discrete Laplacian which accounts only for nearest…
Uniform Strichartz estimates on the lattice
Younghun Hong, Changhun Yang
In this paper, we investigate Strichartz estimates for discrete linear Schrödinger and discrete linear Klein-Gordon equations on a lattice with , where is…
Global existence versus finite time blowup dichotomy for the system of nonlinear Schrödinger equations
Younghun Hong, Soonsik Kwon, Haewon Yoon
We construct an extremizer for the kinetic energy inequality (except the endpoint cases) developing the concentration-compactness technique for operator valued inequality in the fo…
Uniqueness and symmetry of ground states for higher-order equations
Woocheol Choi, Younghun Hong, Jinmyoung Seok
We establish uniqueness and radial symmetry of ground states for higher-order nonlinear Schrödinger and Hartree equations whose higher-order differentials have small coefficients.…
On the Strichartz estimates for orthonormal systems of initial data with regularity
Neal Bez, Younghun Hong, Sanghyuk Lee +2
The classical Strichartz estimates for the free Schrödinger propagator have recently been substantially generalised to estimates of the form \[ \bigg\|\sum_jλ_j|e^{itΔ}f_j|^2\bigg\…
On critical and supercritical pseudo-relativistic nonlinear Schrödinger equations
Woocheol Choi, Younghun Hong, Jinmyoung Seok
In this paper, we investigate existence and non-existence of a nontrivial solution to the pseudo-relativistic nonlinear Schrödinger equation $$\left( \sqrt{-c^2Δ+ m^2 c^4}-mc^2\rig…
Optimal convergence rate of nonrelativistic limit for the nonlinear pseudo-relativistic equations
Woocheol Choi, Younghun Hong, Jinmyoung Seok
In this paper, we are concerned with the nonrelativistic limit of the following pseudo-relativistic equation with Hartree nonlinearity or power type nonlinearity \[ \left(\sqrt{-\h…
On the scattering problem for infinitely many fermions in dimensions at positive temperature
Thomas Chen, Younghun Hong, Nataša Pavlović
In this paper, we study the dynamics of a system of infinitely many fermions in dimensions near thermal equilibrium and prove scattering in the case of small perturbation…
Semilinear elliptic equations with the pseudo-relativistic operator on a bounded domain
Woocheol Choi, Younghun Hong, Jinmyoung Seok
We study the Dirichlet problem for the semilinear equations involving the pseudo-relativistic operator on a bounded domain, (\sqrt{-Δ+ m^2} - m)u =|u|^{p-1}u \quad \textrm{in}~Ω, w…
On dispersive blow-ups for the nonlinear Schrödinger equation
Younghun Hong, Maja Tasković
In this article, we provide a simple method for constructing dispersive blow-up solutions to the nonlinear Schrödinger equation. Our construction mainly follows the approach in Bon…
Global Well-posedness of the NLS System for infinitely many fermions
Thomas Chen, Younghun Hong, Nataša Pavlović
In this paper, we study the mean field quantum fluctuation dynamics for a system of infinitely many fermions with delta pair interactions in the vicinity of an equilibrium solution…
On Fractional Schrodinger Equations in sobolev spaces
Younghun Hong, Yannick Sire
Let with . We investigate the fractional nonlinear Schrödinger equation in : w…
A new class of Traveling Solitons for cubic Fractional Nonlinear Schrodinger equations
Younghun Hong, Yannick Sire
We consider the one-dimensional cubic fractional nonlinear Schrödinger equation where and the operator is the fract…