On rigidity of the steady Ericksen-Leslie system
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910819029090304 |
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| author | Bang, Jeaheang Wang, Changyou |
| author_facet | Bang, Jeaheang Wang, Changyou |
| contents | We study solutions, with scaling-invariant bounds, to the steady simplified Ericksen-Leslie system in $\mathbb{R}^n\setminus \{0\}$. When $n=2$, we construct and classify a class of self-similar solutions. When $n\ge 3$, we establish the rigidity asserting that if $(u,d)$ satisfies a scaling-invariant bound with a small constant, then $u\equiv 0$ and $d=$ constant for $n\geq 4$ or $u$ is a Landau solution and $d=$ constant for $n=3$. Such a smallness condition can be weaken when $n=4$ or the solutions are self-similar. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_05326 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On rigidity of the steady Ericksen-Leslie system Bang, Jeaheang Wang, Changyou Analysis of PDEs We study solutions, with scaling-invariant bounds, to the steady simplified Ericksen-Leslie system in $\mathbb{R}^n\setminus \{0\}$. When $n=2$, we construct and classify a class of self-similar solutions. When $n\ge 3$, we establish the rigidity asserting that if $(u,d)$ satisfies a scaling-invariant bound with a small constant, then $u\equiv 0$ and $d=$ constant for $n\geq 4$ or $u$ is a Landau solution and $d=$ constant for $n=3$. Such a smallness condition can be weaken when $n=4$ or the solutions are self-similar. |
| title | On rigidity of the steady Ericksen-Leslie system |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2502.05326 |