Continuous in time bubble decomposition for the harmonic map heat flow
We consider the harmonic map heat flow for maps $\mathbb {R}^{2} \to \mathbb {S}^2$ . 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...
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Cambridge University Press
2025-01-01
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| Series: | Forum of Mathematics, Pi |
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| Online Access: | https://www.cambridge.org/core/product/identifier/S2050508624000155/type/journal_article |
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| author | Jacek Jendrej Andrew Lawrie Wilhelm Schlag |
| author_facet | Jacek Jendrej Andrew Lawrie Wilhelm Schlag |
| author_sort | Jacek Jendrej |
| collection | DOAJ |
| description | We consider the harmonic map heat flow for maps
$\mathbb {R}^{2} \to \mathbb {S}^2$
. 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 | Article |
| id | doaj-art-7ba0536f8bb543afbc39769aff318c32 |
| institution | Kabale University |
| issn | 2050-5086 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Pi |
| spelling | doaj-art-7ba0536f8bb543afbc39769aff318c322025-02-11T03:30:58ZengCambridge University PressForum of Mathematics, Pi2050-50862025-01-011310.1017/fmp.2024.15Continuous in time bubble decomposition for the harmonic map heat flowJacek Jendrej0Andrew Lawrie1https://orcid.org/0000-0002-9579-5760Wilhelm Schlag2CNRS and LAGA, Université Sorbonne Paris Nord, 99 av Jean-Baptiste Clément, 93430 Neuchâtel, Villetaneuse, France; E-mail:Department of Mathematics, The University of Maryland, 4176 Campus Drive - William E. Kirwan Hall, College Park, MD, 20742-4015, USADepartment of Mathematics, Yale University, 10 Hillhouse Ave, New Haven, CT, 06511, USA; E-mail:We consider the harmonic map heat flow for maps $\mathbb {R}^{2} \to \mathbb {S}^2$ . 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.https://www.cambridge.org/core/product/identifier/S2050508624000155/type/journal_article35K5858J3553E99 |
| spellingShingle | Jacek Jendrej Andrew Lawrie Wilhelm Schlag Continuous in time bubble decomposition for the harmonic map heat flow Forum of Mathematics, Pi 35K58 58J35 53E99 |
| title | Continuous in time bubble decomposition for the harmonic map heat flow |
| title_full | Continuous in time bubble decomposition for the harmonic map heat flow |
| title_fullStr | Continuous in time bubble decomposition for the harmonic map heat flow |
| title_full_unstemmed | Continuous in time bubble decomposition for the harmonic map heat flow |
| title_short | Continuous in time bubble decomposition for the harmonic map heat flow |
| title_sort | continuous in time bubble decomposition for the harmonic map heat flow |
| topic | 35K58 58J35 53E99 |
| url | https://www.cambridge.org/core/product/identifier/S2050508624000155/type/journal_article |
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