On local smoothing estimates for wave equations

Shengwen Gan; Danqing He; Xiaochun Li; Shukun Wu

On local smoothing estimates for wave equations

Analysis of PDEs 2026-01-06 v2 Classical Analysis and ODEs

Authors: Shengwen Gan , Danqing He , Xiaochun Li , Shukun Wu

Abstract

We prove sharp local smoothing estimates for wave equations on compact Riemannian manifolds in $n+1$ dimensions for odd $n$ and obtain improved estimates in even dimensions. This is achieved by deriving local smoothing estimates for certain Fourier integral operators. We also obtain improved local smoothing estimates for wave equations in Euclidean spaces.

Keywords

strichartz estimates gradient estimates wavelet and multifractal analysis

Cite

@article{arxiv.2502.05973,
  title  = {On local smoothing estimates for wave equations},
  author = {Shengwen Gan and Danqing He and Xiaochun Li and Shukun Wu},
  journal= {arXiv preprint arXiv:2502.05973},
  year   = {2026}
}

Comments

Main results improved; Danqing He and Xiaochun Li are now named authors

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