Quantized slow blow-up dynamics for the energy-critical corotational wave maps problem
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866908641878081536 |
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| author | Jeong, Uihyeon |
| author_facet | Jeong, Uihyeon |
| contents | We study the blow-up dynamics for the energy-critical 1-corotational wave maps problem with 2-sphere target. In arXiv:0911.0692, Raphaël and Rodnianski exhibited a stable finite time blow-up dynamics arising from smooth initial data. In this paper, we exhibit a sequence of new finite-time blow-up rates (quantized rates), which can still arise from well-localized smooth initial data. We closely follow the strategy of the paper arXiv:1301.1859 by Raphaël and Schweyer, who exhibited a similar construction of the quantized blow-up rates for the harmonic map heat flow. The main difficulty in our wave maps setting stems from the lack of dissipation and its critical nature, which we overcome by a systematic identification of correction terms in higher-order energy estimates. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2312_16452 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quantized slow blow-up dynamics for the energy-critical corotational wave maps problem Jeong, Uihyeon Analysis of PDEs 35B44 (primary), 35L71, 37K40, 58E20 We study the blow-up dynamics for the energy-critical 1-corotational wave maps problem with 2-sphere target. In arXiv:0911.0692, Raphaël and Rodnianski exhibited a stable finite time blow-up dynamics arising from smooth initial data. In this paper, we exhibit a sequence of new finite-time blow-up rates (quantized rates), which can still arise from well-localized smooth initial data. We closely follow the strategy of the paper arXiv:1301.1859 by Raphaël and Schweyer, who exhibited a similar construction of the quantized blow-up rates for the harmonic map heat flow. The main difficulty in our wave maps setting stems from the lack of dissipation and its critical nature, which we overcome by a systematic identification of correction terms in higher-order energy estimates. |
| title | Quantized slow blow-up dynamics for the energy-critical corotational wave maps problem |
| topic | Analysis of PDEs 35B44 (primary), 35L71, 37K40, 58E20 |
| url | https://arxiv.org/abs/2312.16452 |