Qiuye Jia

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20242026

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11 papers · 1 filter

math.AP2026

Sharp Dispersive Estimates for the Schrödinger Equation with an Attractive Coulomb Potential

Xitao Gao, Qiuye Jia, Junyong Zhang

We prove sharp dispersive $L^{1} \to L^{\infty}$ estimates for the three-dimensional attractive Coulomb operator $H_{Z} = - Δ - Z ∣ x ∣^{- 1}$ , where $Z > 0$ . The absolutely continuous part of the…

math.AP2026

Determining potentials from the scattering map of the time-dependent Schrödinger equation

Qiuye Jia

For a time dependent Schrödinger equation, the scattering map is the map sending the asymptotic profile of a solution as $t \to - \infty$ to its asymptotic profile as $t \to + \infty$ .…

math.AP2026

The effect of geometric focusing on dispersive estimates for the Schrödinger and wave equations

Qiuye Jia, Junyong Zhang

We classify the long-time decay rate in dispersive estimates for the Schrödinger and wave equations on non-trapping asymptotically conic manifolds and exact metric cones in terms o…

math.AP2026

Determining metrics from the scattering map of the time-dependent Schrödinger equation

Qiuye Jia

For a time dependent Schrödinger equation, the scattering map is the map sending the asymptotic profile of solution as $t \to - \infty$ to its asymptotic profile as $t \to + \infty$ . In…

math.AP2026

Lecture notes on non-elliptic Fredholm theory

Andrew Hassell, Qiuye Jia, Ethan Sussman

These are lecture notes from the Austral Winter School on Microlocal Analysis and Non-elliptic Fredholm Theory, held at the Australian National University, Canberra, June 30 -- Jul…

math.AP2026

The scattering map for the Schrodinger operator on curved spaces

Andrew Hassell, Qiuye Jia

Let $P$ be a Schrödinger operator $D_{t} + Δ_{g}$ with metric and potential perturbation that are compactly supported in spacetime $R^{n + 1}$ . Here $D_{t} = - i \partial_{t}$ and $Δ_g…

math.AP2025

Bochner-Riesz means on a conical singular manifold

Qiuye Jia, Junyong Zhang, Jiqiang Zheng

We prove a sharp $L^{p}$ -boundedness criterion for Bochner-Riesz multipliers on flat cones $X = (0, \infty) \times S_{σ}^{1}$ . The operator $S_{λ}^{δ} (Δ_{X})$ is bounded on $L^{p} (X)$ fo…

math.AP2025

Decay and Strichartz estimates for critical electromagnetic wave equations on conic manifolds

Qiuye Jia, Junyong Zhang

We establish the decay and Strichartz estimates for the wave equation with large scaling-critical electromagnetic potentials on a conical singular space $(X, g)$ with dimension $n\g…

math.AP2024

Strichartz estimates for the Schrödinger equation in high dimensional critical electromagnetic fields

Qiuye Jia, Junyong Zhang

We prove Strichartz estimates for the Schrödinger equation with scaling-critical electromagnetic potentials in dimensions $n \geq 3$ . The decay assumption on the magnetic potentials…

math.AP2024

The final state problem for the nonlinear Schrodinger equation in dimensions 1, 2 and 3

Andrew Hassell, Qiuye Jia

In this article we consider the defocusing nonlinear Schrödinger equation, with time-dependent potential, in space dimensions $n = 1, 2$ and $3$ , with nonlinearity $∣ u ∣^{p - 1} u$ , $p$ …

math.AP2024

Pointwise dispersive estimates for Schrodinger and wave equations in a conical singular space

Qiuye Jia, Junyong Zhang

We study the pointwise decay estimates for the Schrödinger and wave equations on a product cone $(X, g)$ , where the metric $g = d r^{2} + r^{2} h$ and $X = C (Y) = (0, \infty) \times Y$ is a produc…