Strichartz estimate for discrete Schr\"odinger equation on layered King's grid

Abstract

We establish the sharp \( l^1 \to l^{\infty} \) decay estimate for the discrete Schr\"odinger 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.