Optimal blowup stability for three-dimensional wave maps
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866913769533210624 |
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| author | Donninger, Roland Wallauch, David |
| author_facet | Donninger, Roland Wallauch, David |
| contents | We study corotational wave maps from $(1+3)$-dimensional Minkowski space into the three-sphere. We establish the asymptotic stability of an explicitly known self-similar wave map under perturbations that are small in the critical Sobolev space. This is accomplished by proving Strichartz estimates for a radial wave equation with a potential in similarity coordinates. Compared to earlier work, the main novelty lies with the fact that the critical Sobolev space is of fractional order. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_08374 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Optimal blowup stability for three-dimensional wave maps Donninger, Roland Wallauch, David Analysis of PDEs Mathematical Physics We study corotational wave maps from $(1+3)$-dimensional Minkowski space into the three-sphere. We establish the asymptotic stability of an explicitly known self-similar wave map under perturbations that are small in the critical Sobolev space. This is accomplished by proving Strichartz estimates for a radial wave equation with a potential in similarity coordinates. Compared to earlier work, the main novelty lies with the fact that the critical Sobolev space is of fractional order. |
| title | Optimal blowup stability for three-dimensional wave maps |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2212.08374 |