8 citations · 49 across the 48 of their papers we have counts for
51 papers
On weighted estimates involving singular weights for the Dirac equation
Seongyeon Kim, Ihyeok Seo
We obtain weighted estimates for solutions to the Dirac equation with weights in the Kerman-Sawyer class. This class has been introduced as a necessary and sufficient conditi…
Remarks on the well-posedness of the energy-critical inhomogeneous Hartree equation
Seongyeon Kim, Tarek Saanouni, Ihyeok Seo
We study the energy-critical inhomogeneous Hartree equation in space dimensions three and higher. Previous local well-posedness results left open the parameter regime where the inh…
On Morawetz estimates for the elastic wave equation
Seongyeon Kim, Ihyeok Seo
We establish Morawetz-type estimates for solutions to the elastic wave equation with singular weights of the form or . In particular, we show that space-ti…
On the radius of spatial analyticity for the Majda-Biello and Hirota-Satsuma systems
Seongyeon Kim, Ihyeok Seo
We investigate the persistence of spatial analyticity for solutions to the Majda-Biello and Hirota-Satsuma systems with analytic initial data. This result is the first to establish…
On Dirac equations with Hartree type nonlinearity in modulation spaces
Seongyeon Kim, Hyeongjin Lee, Ihyeok Seo
We obtain the local well-posedness for Dirac equations with a Hartree type nonlinearity derived by decoupling the Dirac-Klein-Gordon system. We extend the function space of initial…
Explicit inversion for variable-speed wave equations on bounded domains
Sunghwan Moon, Ihyeok Seo
We study the reconstruction of the initial pressure for the wave model \[ \partial_t^2 p(x,t)=c(x)Δ_{x}p(x,t)\qquad (x,t)\inΩ\times[0,\infty), \] posed on a bounded d…
Reconstruction of the initial data from the trace of the solutions on an infinite time cylinder of damped wave equations
Seongyeon Kim, Sunghwan Moon, Ihyeok Seo
In this paper, we consider two types of damped wave equations: the weakly damped equation and the strongly damped equation. We recover the initial velocity from the trace of the so…
Talbot effect for the third order Lugiato-Lefever equation
Gunwoo Cho, Seongyeon Kim, Ihyeok Seo
We discuss the Lugiato-Lefever equation and its variant with third-order dispersion, which are mathematical models used to describe how a light beam forms patterns within an optica…
Phase-shifted Adversarial Training
Yeachan Kim, Seongyeon Kim, Ihyeok Seo +1
Adversarial training has been considered an imperative component for safely deploying neural network-based applications to the real world. To achieve stronger robustness, existing…
On local well-posedness of nonlinear dispersive equations with partially regular data
Youngwoo Koh, Yoonjung Lee, Ihyeok Seo
We revisit the local well-posedness theory of nonlinear Schrödinger and wave equations in Sobolev spaces and , . The theory has been well established o…
Strichartz estimates for the Dirac flow in Wiener amalgam spaces
Seongyeon Kim, Hyeongjin Lee, Ihyeok Seo
In this paper we obtain some new Strichartz estimates for the Dirac flow in the context of Wiener amalgam spaces which control the local regularity of a function and its decay at i…
Global attractor for the weakly damped forced Kawahara equation on the torus
Jaeseop Ahn, Seongyeon Kim, Ihyeok Seo
We study the long time behaviour of solutions for the weakly damped forced Kawahara equation on the torus. More precisely, we prove the existence of a global attractor in , to…
Sharp weighted Strichartz estimates and critical inhomogeneous Hartree equations
Seongyeon Kim, Yoonjung Lee, Ihyeok Seo
We study the Cauchy problem for the inhomogeneous Hartree equation in this paper. Although its well-posedness theory has been extensively studied in recent years, much less is know…
Pointwise convergence for the elastic wave equation
Chu-Hee Cho, Seongyeon Kim, Yehyun Kwon +1
We study pointwise convergence of the solution to the elastic wave equation to the initial data which lies in the Sobolev spaces. We prove that the solution converges along every l…
Quantum revivals and fractality for the Schrödinger equation
Gunwoo Cho, Jimyeong Kim, Seongyeon Kim +2
We investigate the behavior of the Schrödinger equation under the influence of potentials, focusing on its relationship to quantum revivals and fractality. Our findings reveal that…
Strichartz and uniform Sobolev inequalities for the elastic wave equation
Seongyeon Kim, Yehyun Kwon, Sanghyuk Lee +1
We prove dispersive estimate for the elastic wave equation by which we extend the known Strichartz estimates for the classical wave equation to those for the elastic wave equation.…
On the radius of spatial analyticity for the Klein-Gordon-Schrödinger system
Jaeseop Ahn, Jimyeong Kim, Ihyeok Seo
In this paper, we study the persistence of spatial analyticity for the solutions to the Klein-Gordon-Schrödinger system, which describes a physical system of a nucleon field intera…
Strichartz estimates in Wiener amalgam spaces and applications to nonlinear wave equations
Seongyeon Kim, Youngwoo Koh, Ihyeok Seo
In this paper we obtain some new Strichartz estimates for the wave propagator in the context of Wiener amalgam spaces. While it is well understood for the Schrödi…
Strichartz estimates and local regularity for the elastic wave equation with singular potentials
Seongyeon Kim, Yehyun Kwon, Ihyeok Seo
We obtain weighted estimates for the elastic wave equation perturbed by singular potentials including the inverse-square potential. We then deduce the Strichartz estimates un…
Endpoint Strichartz estimates with angular integrability and some applications
Jungkwon Kim, Yoonjung Lee, Ihyeok Seo
The endpoint Strichartz estimate is known to be false in two space dimensions. Taking averages spherically on the polar coor…
Resolvent estimates for the Lamé operator and failure of Carleman estimates
Yehyun Kwon, Sanghyuk Lee, Ihyeok Seo
In this paper, we consider the Lamé operator and study resolvent estimate, uniform Sobolev estimate, and Carleman estimate for . First, we obtain sharp --$L…
On Morawetz estimates with time-dependent weights for the Klein-Gordon equation
Jungkwon Kim, Hyeongjin Lee, Ihyeok Seo +1
We obtain some new Morawetz estimates for the Klein-Gordon flow of the form \begin{equation*} \big\||\nabla|^σ e^{it \sqrt{1-Δ}}f \big\|_{L^2_{x,t}(|(x,t)|^{-α})} \lesssim \|f\|_{H…
The Cauchy problem for the energy-critical inhomogeneous nonlinear Schrödinger equation
Yoonjung Lee, Ihyeok Seo
In this paper we study the Cauchy problem for the energy-critical inhomogeneous nonlinear Schrödinger equation in . The well-posedness theo…
On local-in-time Strichartz estimates for the Schrödinger equation with singular potentials
Seongyeon Kim, Ihyeok Seo, Jihyeon Seok
There have been a lot of works concerning the Strichartz estimates for the perturbed Schrödinger equation by potential. These can be basically carried out adopting the well-known p…