10 papers · 1 filter
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…
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} ),\…