Future stability of large-data wave maps in energy-supercritical dimensions
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908860377202688 |
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| author | Bonk, Andras Donninger, Roland |
| author_facet | Bonk, Andras Donninger, Roland |
| contents | We consider energy-supercritical co-rotational wave maps from Minkowski spacetime to the sphere in odd spatial dimensions. The equation admits an explicit co-rotational self-similar blowup solution, which also induces solutions that blow up in the past. In the region after the blowup the solution treated in this paper is remarkable, as it is smooth forward in time and exhibits less than dispersive decay. We prove nonlinear asymptotic stability of this large-data self-similar solution inside forward light cones. In particular, we identify an open set of initial data close to the explicit solution that give rise to forward-in-time wave maps whose decay is slower than that of generic free waves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_01924 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Future stability of large-data wave maps in energy-supercritical dimensions Bonk, Andras Donninger, Roland Analysis of PDEs Mathematical Physics We consider energy-supercritical co-rotational wave maps from Minkowski spacetime to the sphere in odd spatial dimensions. The equation admits an explicit co-rotational self-similar blowup solution, which also induces solutions that blow up in the past. In the region after the blowup the solution treated in this paper is remarkable, as it is smooth forward in time and exhibits less than dispersive decay. We prove nonlinear asymptotic stability of this large-data self-similar solution inside forward light cones. In particular, we identify an open set of initial data close to the explicit solution that give rise to forward-in-time wave maps whose decay is slower than that of generic free waves. |
| title | Future stability of large-data wave maps in energy-supercritical dimensions |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2603.01924 |