Qiuye Jia

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20242026

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6 papers · 2 filters

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…