arXiv subjects

Jaeseop Ahn

Publications and source records attributed to Jaeseop Ahn.

4 recordsLinked to original sources

arXiv2024

Global attractor for the weakly damped forced Kawahara equation on the torus

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 $L^2$, to which as time passes all solutions draw closer. In fact, we show that the global attractor turns out to lie in a smoother space $H^2$ and be bounded therein. Further, we give an upper bound of the size of the attractor in $H^2$ that depends only on the damping parameter and the norm of the forcing term.

math.AP↗

arXiv2022

On the radius of spatial analyticity for the Klein-Gordon-Schrödinger system

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 interacting with a neutral meson field, with analytic initial data. Unlike the case of a single nonlinear dispersive equation, not much is known about nonlinear dispersive systems as it is harder to show the spatial analyticity of coupled equations simultaneously. The only results known so far are rather recent ones for the Dirac-Klein-Gordon system which governs the physical system when the nucleon is described by Dirac spinor fields in the case of relativistic fields. In contrast, we aim here to study the Klein-Gordon-Schrödinger system that works in the non-relativistic regime. It is shown that the radius of spatial analyticity of the solutions at later times obeys an algebraic lower bound as time goes to infinity.

math.AP↗

arXiv2020

Lower bounds on the radius of spatial analyticity for the Kawahara equation

In this paper we obtain lower bounds on the radius of spatial analyticity of solutions to the Kawahara equation $u_t + uu_x + αu_{xxx} + βu_{xxxxx} = 0$, $β\neq0$, given initial data which is analytic with a fixed radius. It is shown that the uniform radius of spatial analyticity of solutions at later time $t$ can decay no faster than $1/|t|$ as $|t|\rightarrow\infty$.

math.AP↗

arXiv2019

On the radius of spatial analyticity for defocusing nonlinear Schrödinger equations

In this paper we study spatial analyticity of solutions to the defocusing nonlinear Schrödinger equations $iu_t + Δu = |u|^{p-1}u$, given initial data which is analytic with fixed radius. It is shown that the uniform radius of spatial analyticity of solutions at later time $t$ cannot decay faster than $1/|t|$ as $|t|\rightarrow\infty$. This extends the previous work of Tesfahun for the cubic case $p=3$ to the cases where $p$ is any odd integer greater than $3$.

math.AP↗