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arXiv · 2510.06958

On Morawetz estimates for the elastic wave equation

Seongyeon Kim·Ihyeok Seo
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Abstract

We establish Morawetz-type estimates for solutions to the elastic wave equation with singular weights of the form $|x|^{-\alpha}$ or $|(x,t)|^{-\alpha}$. In particular, we show that space-time weights $|(x,t)|^{-\alpha}$ admit stronger singularities and require weaker regularity assumptions on the initial data compared to purely spatial weights $|x|^{-\alpha}$.

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Seongyeon Kim, Ihyeok Seo. 2025-10-08. On Morawetz estimates for the elastic wave equation. https://arxiv.org/abs/2510.06958

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