Year: 2025
Type: preprint
Abstract: We establish the sharp \( l^1 \to l^{\infty} \) decay estimate for the discrete Schrödinger equation (DS) on the Layered King's Grid (LKG), with a dispersive decay rate of \( \langle t \rangle^{-13/12} \), which is faster than that for $3$-dimensional lattice (\( \langle t \rangle^{-1} \), see \cite{SK05}). This decay estimate enables us to derive the corresponding Strichartz estimate via the standard Keel--Tao argument. Our approach relies on using techniques from Newton polyhedra to analyze singularities.
Source: arXiv (Cornell University)
Authors: Wan, Zhiqiang, Zhang, Heng
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7077039335
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