Xuan Liu

collaborators

3 papers

math.AP2025

The defocusing energy-supercritical inhomogeneous NLS in four space dimension

Xuan Liu, Chengbin Xu

In this paper, we investigate the global well-posedness and scattering theory for the defocusing energy supcritical inhomogeneous nonlinear Schrödinger equation $iu_t + Δu =|x|^{-b…

math.AP2025

Scattering theory for the defocusing 3d NLS in the exterior of a strictly convex obstacle

Xuan Liu, Yilin Song, Jiqiang Zheng

In this paper, we investigate the global well-posedness and scattering theory for the defocusing nonlinear Schrödinger equation $i u_{t} + Δ_{Ω} u = ∣ u ∣^{α} u$ in the exterior domain $Ω$ of…

math.AP2024

Global well-posedness and scattering for mass-critical inhomogeneous NLS when $d \geq 3$

Xuan Liu, Changxing Miao, Jiqiang Zheng

We prove global well-posedness and scattering for solutions to the mass-critical inhomogeneous nonlinear Schrödinger equation $i \partial_{t} u + Δ u = \pm ∣ x ∣^{- b} ∣ u ∣^{\frac{4 - 2 b}{d}} u$ …

The defocusing energy-supercritical inhomogeneous NLS in four space dimension

Scattering theory for the defocusing 3d NLS in the exterior of a strictly convex obstacle

Global well-posedness and scattering for mass-critical inhomogeneous NLS when d≥3

Global well-posedness and scattering for mass-critical inhomogeneous NLS when $d \geq 3$