25 citations · 32 across the 16 of their papers we have counts for
16 papers
Regular Strichartz estimates in Lorentz-type spaces with application to the -critical inhomogeneous biharmonic NLS equation
RoeSong Jang, JinMyong An, JinMyong Kim
In this paper, we investigate the Cauchy problem for the -critical inhomogeneous biharmonic nonlinear Schrödinger (IBNLS) equation \[iu_{t}\pm Δ^{2} u=λ|x|^{-b}|u|^σu,~u(0)=u_…
On the Cauchy problem for the inhomogeneous nonlinear Schrödinger equation with inverse-power potential
JinMyong An, JinMyong Kim, OkByol Kim
In this paper, we study the Cauchy problem for the inhomogeneous nonlinear Schrödinger equation with inverse-power potential \[iu_{t} +Δu-c|x|^{-a}u=\pm |x|^{-b} |u|^{σ} u,\;\;(t,x…
On stability and instability of the ground states for the focusing inhomogeneous NLS with inverse-square potential
JinMyong An, HakBom Mun, JinMyong Kim
In this paper, we study the stability and instability of the ground states for the focusing inhomogeneous nonlinear Schrödinger equation with inverse-square potential (for short, I…
Continuous dependence of the Cauchy problem for the inhomogeneous biharmonic NLS equation in Sobolev spaces
JinMyong An, YuIl Jo, JinMyong Kim
In this paper, we study the continuous dependence of the Cauchy problem for the inhomogeneous biharmonic nonlinear Schrödinger (IBNLS) equation \[iu_{t} +Δ^{2} u=λ|x|^{-b}|u|^σu,~u…
Sobolev-Lorentz spaces with an application to the inhomogeneous biharmonic NLS equation
JinMyong An, PyongJo Ryu, JinMyong Kim
We consider the Cauchy problem for the inhomogeneous biharmonic nonlinear Schrödinger (IBNLS) equation \[iu_{t} +Δ^{2} u=λ|x|^{-b}|u|^σu,\;u(0)=u_{0} \in H^{s} (\mathbb R^{d}),\] w…
Small data global well-posedness for the inhomogeneous biharmonic NLS in Sobolev spaces
JinMyong An, PyongJo Ryu, JinMyong Kim
In this paper, we study the Cauchy problem for the inhomogeneous biharmonic nonlinear Schrödinger equation (IBNLS) \[iu_{t} +Δ^{2} u=λ|x|^{-b}|u|^σu,u(0)=u_{0} \in H^{s} (\mathbb R…
Local well-posedness for the inhomogeneous biharmonic nonlinear Schrödinger equation in Sobolev spaces
JinMyong An, PyongJo Ryu, JinMyong Kim
In this paper, we study the Cauchy problem for the inhomogeneous biharmonic nonlinear Schrödinger (IBNLS) equation \[iu_{t} +Δ^{2} u=λ|x|^{-b}|u|^σu,~u(0)=u_{0} \in H^{s} (\mathbb…
A note on the -critical inhomogeneous nonlinear Schrödinger equation
JinMyong An, JinMyong Kim
In this paper, we consider the Cauchy problem for the -critical inhomogeneous nonlinear Schrödinger (INLS) equation \[iu_{t} +Δu=λ|x|^{-b} f(u),\; u(0)=u_{0} \in H^{s} (\mat…
Global existence and blow-up for the focusing inhomogeneous nonlinear Schrödinger equation with inverse-square potential
JinMyong An, JinMyong Kim, RoeSong Jang
In this paper, we study the Cauchy problem for the focusing inhomogeneous nonlinear Schrödinger equation with inverse-square potential \[iu_{t} +Δu-c|x|^{-2}u+|x|^{-b} |u|^{σ} u=0,…
The Cauchy problem for the critical inhomogeneous nonlinear Schrödinger equation in
JinMyong An, JinMyong Kim
In this paper, we study the Cauchy problem for the critical inhomogeneous nonlinear Schrödinger (INLS) equation \[iu_{t} +Δu=|x|^{-b} f(u), ~u(0)=u_{0} \in H^{s} (\mathbb R^{n} ),\…
Continuous dependence of the Cauchy problem for the inhomogeneous nonlinear Schrödinger equation in
JinMyong An, JinMyong Kim, KyuSong Chae
We consider the Cauchy problem for the inhomogeneous nonlinear Schrödinger (INLS) equation \[iu_{t} +Δu=|x|^{-b} f(u),\;u(0)\in H^{s} (\mathbb R^{n} ),\] where , $0…
Small data global well--posedness and scattering for the inhomogeneous nonlinear Schrödinger equation in
JinMyong An, JinMyong Kim
We consider the Cauchy problem for the inhomogeneous nonlinear Schrödinger (INLS) equation \[iu_{t} +Δu=|x|^{-b} f\left(u\right), u\left(0\right)=u_{0} \in H^{s} (\mathbb R^{n}),\]…
Local and global well-posedness in for the inhomogeneous nonlinear Schrödinger equation
JinMyong An, JinMyong Kim
This paper investigates the local and global well-posedness for the inhomogeneous nonlinear Schrödinger (INLS) equation $iu_{t} +Δu=λ\left|x\right|^{-b} \left|u\right|^{σ} u, u(0)=…
The Cauchy problem for the energy-critical inhomogeneous nonlinear Schrödinger equation with inverse-square potential
RoeSong Jang, JinMyong An, JinMyong Kim
In this paper, we study the Cauchy problem for the energy-critical inhomogeneous nonlinear Schrödinger equation with inverse-square potential \[iu_{t} +Δu-c|x|^{-2}u=λ|x|^{-b} |u|^…
Estimates for a class of oscillatory integrals and decay rates for wave-type equations
Anton Arnold, JinMyong Kim, Xiaohua Yao
This paper investigates higher order wave-type equations of the form , where the symbol is a real, non-degenerate elliptic polynomial of the orde…
Global estimates of fundamental solutions for higher-order Schrödinger equations
JinMyong Kim, Anton Arnold, Xiaohua Yao
In this paper we first establish global pointwise time-space estimates of the fundamental solution for Schrödinger equations, where the symbol of the spatial operator is a real non…