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math.AP2022
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…
math.AP2022
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…
math.AP2022
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…