Abstract
In this article we prove a Sacks-Uhlenbeck/Struwe type global regularity result for wave-maps \({\Phi:\mathbb{R}^{2+1} \to\mathcal{M} }\) into general compact target manifolds \({\mathcal{M} }\).
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Acknowledgements
The authors would like to thank Manos Grillakis, Sergiu Klainerman, Joachim Krieger, Matei Machedon, Igor Rodnianski, and Wilhelm Schlag for many stimulating discussions over the years regarding the wave-map problem. We would also especially like to thank Terry Tao for several key discussions on the nature of induction-on-energy type proofs.
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Communicated by P. Constantin
The first author was supported in part by the NSF grant DMS-0701087.
The second author was supported in part by the NSF grant DMS-0801261.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Sterbenz, J., Tataru, D. Regularity of Wave-Maps in Dimension 2 + 1. Commun. Math. Phys. 298, 231–264 (2010). https://doi.org/10.1007/s00220-010-1062-3
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DOI: https://doi.org/10.1007/s00220-010-1062-3