Rigorous uniaxial limit of the Qian--Sheng inertial Q-tensor hydrodynamics for liquid crystals
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916080315793408 |
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| author | Li, Sirui Wang, Wei Zeng, Qi |
| author_facet | Li, Sirui Wang, Wei Zeng, Qi |
| contents | This article is concerned with the rigorous connections between the inertial Qian--Sheng model and the Ericksen--Leslie model for the liquid crystal flow, under a more general condition of coefficients. More specifically, in the framework of Hilbert expansions, we show that: (i) when the elastic coefficients tend to zero (also called the uniaxial limit), the smooth solution to the inertial Qian--Sheng model converges to that to the full inertial Ericksen--Leslie model; (ii) when the elastic coefficients and the inertial coefficient tend to zero simultaneously, the smooth solution to the inertial Qian--Sheng model converges to that to the noninertial Ericksen--Leslie model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_01509 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rigorous uniaxial limit of the Qian--Sheng inertial Q-tensor hydrodynamics for liquid crystals Li, Sirui Wang, Wei Zeng, Qi Analysis of PDEs This article is concerned with the rigorous connections between the inertial Qian--Sheng model and the Ericksen--Leslie model for the liquid crystal flow, under a more general condition of coefficients. More specifically, in the framework of Hilbert expansions, we show that: (i) when the elastic coefficients tend to zero (also called the uniaxial limit), the smooth solution to the inertial Qian--Sheng model converges to that to the full inertial Ericksen--Leslie model; (ii) when the elastic coefficients and the inertial coefficient tend to zero simultaneously, the smooth solution to the inertial Qian--Sheng model converges to that to the noninertial Ericksen--Leslie model. |
| title | Rigorous uniaxial limit of the Qian--Sheng inertial Q-tensor hydrodynamics for liquid crystals |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2401.01509 |