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20212024
most citedA note on the -critical inhomogeneous nonlinear Schrödinger equation

2 citations · 2 across the 15 of their papers we have counts for

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math.AP2021★ 2 cited

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…

math.AP2021

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,…

math.AP2021

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} ),\…

math.AP2021

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…

math.AP2021

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 \[iu_{t} +Δu=|x|^{-b} f\left(u\right), u\left(0\right)=u_{0} \in H^{s} (\mathbb R^{n}),\]…

math.AP2021

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)=…

math.AP2021

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|^…

math.ST2021

Sample variance of rounded variables

J. An

If the rounding errors are assumed to be distributed independently from the intrinsic distribution of the random variable, the sample variance of the rounded variable is give…