Well-posedness of half-harmonic map heat flows for rough initial data
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914043590082560 |
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| author | Koch, Kilian Melcher, Christof |
| author_facet | Koch, Kilian Melcher, Christof |
| contents | We adopt the Koch-Tataru theory for the Navier-Stokes equations, based on Carleson measure estimates, to develop a scaling-critical low-regularity framework for half-harmonic map heat flows. This nonlocal variant of the harmonic map heat flow has been studied recently in connection with free boundary minimal surfaces. We introduce a new class of initial data for the flow, broader than the conventional energy or Sobolev spaces considered in previous work, for which we establish existence, uniqueness, and continuous dependence. The class particularly includes homogeneous initial data that give rise to self-similar expanders. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_06933 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Well-posedness of half-harmonic map heat flows for rough initial data Koch, Kilian Melcher, Christof Analysis of PDEs 35K55, 35R11, 58J35, 35A01 We adopt the Koch-Tataru theory for the Navier-Stokes equations, based on Carleson measure estimates, to develop a scaling-critical low-regularity framework for half-harmonic map heat flows. This nonlocal variant of the harmonic map heat flow has been studied recently in connection with free boundary minimal surfaces. We introduce a new class of initial data for the flow, broader than the conventional energy or Sobolev spaces considered in previous work, for which we establish existence, uniqueness, and continuous dependence. The class particularly includes homogeneous initial data that give rise to self-similar expanders. |
| title | Well-posedness of half-harmonic map heat flows for rough initial data |
| topic | Analysis of PDEs 35K55, 35R11, 58J35, 35A01 |
| url | https://arxiv.org/abs/2504.06933 |