Stable blowup for supercritical wave maps into perturbed spheres
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915184329621504 |
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| author | Donninger, Roland Schörkhuber, Birgit Wittenstein, Alexander |
| author_facet | Donninger, Roland Schörkhuber, Birgit Wittenstein, Alexander |
| contents | We consider wave maps from $(1+d)$-dimensional Minkowski space, $d\geq3$, into rotationally symmetric manifolds which arise from small perturbations of the sphere $\mathbb S^d$. We prove the existence of co-rotational self-similar finite time blowup solutions with smooth blowup profiles. Furthermore, we show the nonlinear asymptotic stability of these solutions under suitably small co-rotational perturbations on the full space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_04425 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stable blowup for supercritical wave maps into perturbed spheres Donninger, Roland Schörkhuber, Birgit Wittenstein, Alexander Analysis of PDEs Classical Analysis and ODEs Functional Analysis We consider wave maps from $(1+d)$-dimensional Minkowski space, $d\geq3$, into rotationally symmetric manifolds which arise from small perturbations of the sphere $\mathbb S^d$. We prove the existence of co-rotational self-similar finite time blowup solutions with smooth blowup profiles. Furthermore, we show the nonlinear asymptotic stability of these solutions under suitably small co-rotational perturbations on the full space. |
| title | Stable blowup for supercritical wave maps into perturbed spheres |
| topic | Analysis of PDEs Classical Analysis and ODEs Functional Analysis |
| url | https://arxiv.org/abs/2503.04425 |