Logarithmic wave decay for short range wavespeed perturbations with radial regularity
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915489273348096 |
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| author | Jayasinghe, Gayana Morgan, Katrina Shapiro, Jacob Yang, Mengxuan |
| author_facet | Jayasinghe, Gayana Morgan, Katrina Shapiro, Jacob Yang, Mengxuan |
| contents | We establish logarithmic local energy decay for wave equations with a varying wavespeed in dimensions two and higher, where the wavespeed is assumed to be a short range perturbation of unity with mild radial regularity. The key ingredient is Hölder continuity of the weighted resolvent for real frequencies $λ$, modulo a logarithmic remainder in dimension two as $λ\to 0$. Our approach relies on a study of the resolvent in two distinct frequency regimes. In the low frequency regime, we derive an expansion for the resolvent using a Neumann series and properties of the free resolvent. For frequencies away from zero, we establish a uniform resolvent estimate by way of a Carleman estimate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_08957 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Logarithmic wave decay for short range wavespeed perturbations with radial regularity Jayasinghe, Gayana Morgan, Katrina Shapiro, Jacob Yang, Mengxuan Analysis of PDEs We establish logarithmic local energy decay for wave equations with a varying wavespeed in dimensions two and higher, where the wavespeed is assumed to be a short range perturbation of unity with mild radial regularity. The key ingredient is Hölder continuity of the weighted resolvent for real frequencies $λ$, modulo a logarithmic remainder in dimension two as $λ\to 0$. Our approach relies on a study of the resolvent in two distinct frequency regimes. In the low frequency regime, we derive an expansion for the resolvent using a Neumann series and properties of the free resolvent. For frequencies away from zero, we establish a uniform resolvent estimate by way of a Carleman estimate. |
| title | Logarithmic wave decay for short range wavespeed perturbations with radial regularity |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2509.08957 |