Remarks of global wellposedness of liquid crystal flows and heat flows of harmonic maps in two dimensions
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Bibliographic record
Abstract
We consider the Cauchy problem to the two-dimensional incompressible liquid crystal equation and the heat flows of the harmonic maps equation. Under a natural geometric angle condition, we give a new proof of the global wellposedness of smooth solutions for a class of large initial data in energy space. This result was originally obtained by Ding-Lin and Lin-Lin-Wang. Our main technical tool is a rigidity theorem which gives the coercivity of the harmonic energy under a certain angle condition. Our proof is based on a frequency localization argument combined with the concentration-compactness approach which can be of independent interest.
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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