On Morawetz estimates for the elastic wave equation
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911499929255936 |
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| author | Kim, Seongyeon Seo, Ihyeok |
| author_facet | Kim, Seongyeon Seo, Ihyeok |
| contents | We establish Morawetz-type estimates for solutions to the elastic wave equation with singular weights of the form $|x|^{-α}$ or $|(x,t)|^{-α}$. In particular, we show that space-time weights $|(x,t)|^{-α}$ admit stronger singularities and require weaker regularity assumptions on the initial data compared to purely spatial weights $|x|^{-α}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_06958 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Morawetz estimates for the elastic wave equation Kim, Seongyeon Seo, Ihyeok Analysis of PDEs We establish Morawetz-type estimates for solutions to the elastic wave equation with singular weights of the form $|x|^{-α}$ or $|(x,t)|^{-α}$. In particular, we show that space-time weights $|(x,t)|^{-α}$ admit stronger singularities and require weaker regularity assumptions on the initial data compared to purely spatial weights $|x|^{-α}$. |
| title | On Morawetz estimates for the elastic wave equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2510.06958 |