Strichartz estimate for discrete Schrödinger equation on layered King's grid

2025/07/27 by Wan, Zhiqiang, Zhang, Heng
#Analysis of PDEs (math.AP) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.20142

Abstract

We establish the sharp \( l¹ → l^∞ \) decay estimate for the discrete Schrödinger equation (DS) on the Layered King's Grid (LKG), with a dispersive decay rate of \( ⟨ t ⟩^-13/12 \), which is faster than that for 3-dimensional lattice (\( ⟨ t ⟩^-1 \), see \citeSK05). 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.

Citations

• Continuum Schroedinger operators for sharply terminated graphene-like structures
• Dispersive estimates for quantum walks on 1D lattice
• Honeycomb Lattice Potentials and Dirac Points
• Uniform estimates for the Fourier transform of surface carried measures in \Bbb R³ and an application to Fourier restriction
• On asymptotic stability of standing waves of discrete Schrödinger equation in \Bbb Z

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