Author

Jun-Yong Zhang

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Preprint Sep 2026

A sharp regularity threshold for Schr\"odinger maximal estimates on standard tori

We disprove almost everywhere convergence of the Schr\"odinger evolution on the standard torus $\mathbb{T}^d$ for initial data $f\in H^s(\mathbb{T}^d)$ when $s<d/(d+2)$, in all dimensions $d\ge2$. We construct normalized data with frequencies of size $N$ whose evolution attains size $N^{d/(d+2)}$ on a set of un...

Xi Cen, Xi-Tao Gao, Jun-Yong Zhang · 1 citation · ⚡1

Preprint Sep 2026

$L^p$ bounds for wave operators with critical electromagnetic potentials

We study the M\o ller wave operators for scaling critical electromagnetic Hamiltonians in the plane. For smooth transverse magnetic and angular electric potentials, with nonnegative angular operator and magnetic flux outside $\frac12\Z$, we prove that the wave operators relative to $-\Delta$ exist, are unitary on $L^2$...

Piero D'Ancona, Xi-Tao Gao, Jun-Yong Zhang · 1 citation