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| Format: | Preprint |
| Published: |
2024
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| Online Access: | https://arxiv.org/abs/2401.16824 |
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| _version_ | 1866917578014720000 |
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| author | Su, Xiangxiang |
| author_facet | Su, Xiangxiang |
| contents | We are concerned with the sharp interface limit for the Beris-Edward system in a bounded domain $Ω\subset \mathbb{R}^3$ in this paper. The system can be described as the incompressible Navier-Stokes equations coupled with an evolution equation for the Q-tensor. We prove that the solutions to the Beris-Edward system converge to the corresponding solutions of a sharp interface model under well-prepared initial data, as the thickness of the diffuse interfacial zone tends to zero. Moreover, we give not only the spatial decay estimates of the velocity vector field in the $H^1$ sense but also the error estimates of the phase field. The analysis relies on the relative entropy method and elaborated energy estimates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_16824 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nematic-Isotropic phase transition in Beris-Edward system at critical temperature Su, Xiangxiang Analysis of PDEs We are concerned with the sharp interface limit for the Beris-Edward system in a bounded domain $Ω\subset \mathbb{R}^3$ in this paper. The system can be described as the incompressible Navier-Stokes equations coupled with an evolution equation for the Q-tensor. We prove that the solutions to the Beris-Edward system converge to the corresponding solutions of a sharp interface model under well-prepared initial data, as the thickness of the diffuse interfacial zone tends to zero. Moreover, we give not only the spatial decay estimates of the velocity vector field in the $H^1$ sense but also the error estimates of the phase field. The analysis relies on the relative entropy method and elaborated energy estimates. |
| title | Nematic-Isotropic phase transition in Beris-Edward system at critical temperature |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2401.16824 |