Rigidity of the multi-bubble solutions to the energy critical wave equation in dimension five
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866911723597856768 |
|---|---|
| author | Jendrej, Jacek Zhang, Chencheng Zhao, Lifeng |
| author_facet | Jendrej, Jacek Zhang, Chencheng Zhao, Lifeng |
| contents | We study the asymptotic dynamics of multi-bubble solutions to the focusing energy-critical wave equation in five dimensions. Assuming that the solution asymptotically decomposes into a finite superposition of spatially separated bubbles with comparable scales, we prove a rigidity result that describes the precise long-time behavior of these scales.
More precisely, we show that all scaling parameters are necessarily of order $t^{-2}$, and that the corresponding renormalized modulation vector converges to a connected component of a finite-dimensional algebraic set determined by the limiting spatial configuration of the bubbles. This algebraic system encodes the strong interactions between the polynomial tails of the bubbles and governs the effective asymptotic dynamics of the multi-bubble regime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_27994 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Rigidity of the multi-bubble solutions to the energy critical wave equation in dimension five Jendrej, Jacek Zhang, Chencheng Zhao, Lifeng Analysis of PDEs 35B40 (primary), 35L05, 35B33, 35C08 We study the asymptotic dynamics of multi-bubble solutions to the focusing energy-critical wave equation in five dimensions. Assuming that the solution asymptotically decomposes into a finite superposition of spatially separated bubbles with comparable scales, we prove a rigidity result that describes the precise long-time behavior of these scales. More precisely, we show that all scaling parameters are necessarily of order $t^{-2}$, and that the corresponding renormalized modulation vector converges to a connected component of a finite-dimensional algebraic set determined by the limiting spatial configuration of the bubbles. This algebraic system encodes the strong interactions between the polynomial tails of the bubbles and governs the effective asymptotic dynamics of the multi-bubble regime. |
| title | Rigidity of the multi-bubble solutions to the energy critical wave equation in dimension five |
| topic | Analysis of PDEs 35B40 (primary), 35L05, 35B33, 35C08 |
| url | https://arxiv.org/abs/2605.27994 |