Global strong solutions to the frame hydrodynamics for biaxial nematic phases
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913980626239488 |
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| author | Feng, Minjiang Li, Sirui Zeng, Qi |
| author_facet | Feng, Minjiang Li, Sirui Zeng, Qi |
| contents | In this article, we consider the frame hydrodynamics of biaxial nematic phases, a coupled system between the evolution of the orthonormal frame and the Navier--Stokes equation, which is derived from a molecular-theory-based dynamical tensor model about two second-order tensors. In two and three dimensions, we establish global well-posedness of strong solutions to the Cauchy problem of frame hydrodynamics for small initial data. The key ingredient of the proof relies on estimates of nonlinear terms with rotational derivatives on $SO(3)$, together with the dissipative structure of the frame hydrodynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_06376 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global strong solutions to the frame hydrodynamics for biaxial nematic phases Feng, Minjiang Li, Sirui Zeng, Qi Analysis of PDEs In this article, we consider the frame hydrodynamics of biaxial nematic phases, a coupled system between the evolution of the orthonormal frame and the Navier--Stokes equation, which is derived from a molecular-theory-based dynamical tensor model about two second-order tensors. In two and three dimensions, we establish global well-posedness of strong solutions to the Cauchy problem of frame hydrodynamics for small initial data. The key ingredient of the proof relies on estimates of nonlinear terms with rotational derivatives on $SO(3)$, together with the dissipative structure of the frame hydrodynamics. |
| title | Global strong solutions to the frame hydrodynamics for biaxial nematic phases |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2508.06376 |