7 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_…
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)=…