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arXiv · 2502.05973

On local smoothing estimates for wave equations

Shengwen Gan·Danqing He·Xiaochun Li·Shukun Wu
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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.

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Shengwen Gan, Danqing He, Xiaochun Li, Shukun Wu. 2025-02-09. On local smoothing estimates for wave equations. https://arxiv.org/abs/2502.05973

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