Channels of Energy for the Linearized Energy Critical Wave Equation in Even Dimensions $N\geq 8$
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912322438561792 |
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| author | Hip, Andres A. Contreras |
| author_facet | Hip, Andres A. Contreras |
| contents | We prove an exterior energy estimate for the linearized energy critical wave equation around a multisoliton for even dimensions $N\geq 8.$ This extends previous work of Collot-Duyckaerts-Kenig-Merle to higher dimensions. During the proof we encounter various additional important technical difficulties compared to lower dimensions. In particular, we need to deal with a number of generalized eigenfunctions of the static operator which increases linearly in $N.$ This makes the analysis of projections onto these eigenfunctions a higher dimensional problem, which requires linear systems to control. This is a crucial ingredient in our upcoming work where we give an alternative proof of the soliton resolution for the wave maps equation based on the method of channels of energy developed by Duyckaerts-Kenig-Merle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_09127 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Channels of Energy for the Linearized Energy Critical Wave Equation in Even Dimensions $N\geq 8$ Hip, Andres A. Contreras Analysis of PDEs We prove an exterior energy estimate for the linearized energy critical wave equation around a multisoliton for even dimensions $N\geq 8.$ This extends previous work of Collot-Duyckaerts-Kenig-Merle to higher dimensions. During the proof we encounter various additional important technical difficulties compared to lower dimensions. In particular, we need to deal with a number of generalized eigenfunctions of the static operator which increases linearly in $N.$ This makes the analysis of projections onto these eigenfunctions a higher dimensional problem, which requires linear systems to control. This is a crucial ingredient in our upcoming work where we give an alternative proof of the soliton resolution for the wave maps equation based on the method of channels of energy developed by Duyckaerts-Kenig-Merle. |
| title | Channels of Energy for the Linearized Energy Critical Wave Equation in Even Dimensions $N\geq 8$ |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2504.09127 |