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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.01823 |
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| _version_ | 1866915768569954304 |
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| author | Chen, Yubo Wang, Wendong Wei, Juncheng Yang, Guoxu |
| author_facet | Chen, Yubo Wang, Wendong Wei, Juncheng Yang, Guoxu |
| contents | As is well known, for the harmonic heat flow or liquid crystal flow in two-dimension, the solution may blow up when the initial energy is greater than $8π$. Motivated by Lai--Lin--Wang--Wei--Zhou (CPAM, 2022), where singular solutions were constructed in the presence of small-scale velocity fields, it is natural to ask whether large-scale velocities may play a stabilizing role, preventing the concentration of blow-up. Here we show that the blow-up phenomenon can be suppressed by a Couette flow whose amplitude is large enough under a weak assumption on the anisotropic norm of the initial data. In particular, we construct examples with initial energy exceeding $8π$ that satisfy our assumptions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_01823 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Blow-up suppression for the nematic liquid crystal flow via Couette flow on $\mathbb{R}^2$ Chen, Yubo Wang, Wendong Wei, Juncheng Yang, Guoxu Analysis of PDEs As is well known, for the harmonic heat flow or liquid crystal flow in two-dimension, the solution may blow up when the initial energy is greater than $8π$. Motivated by Lai--Lin--Wang--Wei--Zhou (CPAM, 2022), where singular solutions were constructed in the presence of small-scale velocity fields, it is natural to ask whether large-scale velocities may play a stabilizing role, preventing the concentration of blow-up. Here we show that the blow-up phenomenon can be suppressed by a Couette flow whose amplitude is large enough under a weak assumption on the anisotropic norm of the initial data. In particular, we construct examples with initial energy exceeding $8π$ that satisfy our assumptions. |
| title | Blow-up suppression for the nematic liquid crystal flow via Couette flow on $\mathbb{R}^2$ |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2602.01823 |