arXiv subjects

Tiklung Chan

Publications and source records attributed to Tiklung Chan.

3 recordsLinked to original sources

arXiv2026

Scattering for the Klein-Gordon-Schr\"odinger system in three dimensions with radial data

We prove global well-posedness and scattering for the 3D Klein-Gordon-Schr\"odinger system for small radial data in the best known global well-posedness range $(u_0, n_0, n_1)\in L^2\times H^{ -\frac{1}{2} + \epsilon } \times H^{-\frac{3}{2} +\epsilon }$ for any $ \epsilon > 0 $. The proof uses a global-in-time iteration scheme in the adapted function spaces $U^2_\Phi$, radial Strichartz estimates, and bilinear restriction estimates.

math.AP↗

arXiv2025

Restriction and Kakeya maximal estimates in $\mathbb{R}^4$

By combining the planebrush argument of Katz and Zahl \cite{katz21} with the decoupling-incidence method of Wang and Wu \cite{WangWu2024}, we derive new bounds for the Fourier restriction problem and the Bochner--Riesz problem, extending the range to $p > 2 + \frac{200}{251}$ in $\mathbb{R}^4$. Moreover, leveraging the two-ends Furstenberg estimate in the plane, we also obtain a Kakeya maximal estimate in $\mathbb{R}^4$ at dimension $3.054$.

math.CA↗

arXiv2024

A study guide for the $\ell^2$ decoupling theorem for the paraboloid

This article serves as a study guide for the $\ell^2$ decoupling theorem for the paraboloid originally proved by Bourgain and Demeter. Given its popularity and importance, many expositions about the $\ell^2$ decoupling theorem already exist. Our study guide is intended to complement and combine these existing resources in order to provide a more gentle introduction to the subject.

math.CA↗