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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2304.05927 |
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| _version_ | 1866916619486232576 |
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| author | Jendrej, Jacek Lawrie, Andrew Schlag, Wilhelm |
| author_facet | Jendrej, Jacek Lawrie, Andrew Schlag, Wilhelm |
| contents | We consider the harmonic map heat flow for maps from the plane to the two-sphere. It is known that solutions to the initial value problem exhibit bubbling along a well-chosen sequence of times. We prove that every sequence of times admits a subsequence along which bubbling occurs. This is deduced as a corollary of our main theorem, which shows that the solution approaches the family of multi-bubble configurations in continuous time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_05927 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Continuous in time bubble decomposition for the harmonic map heat flow Jendrej, Jacek Lawrie, Andrew Schlag, Wilhelm Analysis of PDEs Differential Geometry We consider the harmonic map heat flow for maps from the plane to the two-sphere. It is known that solutions to the initial value problem exhibit bubbling along a well-chosen sequence of times. We prove that every sequence of times admits a subsequence along which bubbling occurs. This is deduced as a corollary of our main theorem, which shows that the solution approaches the family of multi-bubble configurations in continuous time. |
| title | Continuous in time bubble decomposition for the harmonic map heat flow |
| topic | Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2304.05927 |