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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.01181 |
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| _version_ | 1866909796540612608 |
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| author | Brandt, Felix Hieber, Matthias Roy, Arnab |
| author_facet | Brandt, Felix Hieber, Matthias Roy, Arnab |
| contents | In this article, the fluid-rigid body interaction problem of nematic liquid crystals described by the general Beris-Edwards $Q$-tensor model is studied. It is proved first that the total energy of this problem decreases in time. The associated mathematical problem is a quasilinear mixed-order system with moving boundary. After the transformation to a fixed domain, a monolithic approach based on the added mass operator and lifting arguments is employed to establish the maximal $L^p$-regularity of the linearized problem in an anisotropic ground space. This paves the way for the local strong well-posedness for large data and global strong well-posedness for small data of the interaction problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_01181 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dynamics of the general $Q$-tensor model interacting with a rigid body Brandt, Felix Hieber, Matthias Roy, Arnab Analysis of PDEs In this article, the fluid-rigid body interaction problem of nematic liquid crystals described by the general Beris-Edwards $Q$-tensor model is studied. It is proved first that the total energy of this problem decreases in time. The associated mathematical problem is a quasilinear mixed-order system with moving boundary. After the transformation to a fixed domain, a monolithic approach based on the added mass operator and lifting arguments is employed to establish the maximal $L^p$-regularity of the linearized problem in an anisotropic ground space. This paves the way for the local strong well-posedness for large data and global strong well-posedness for small data of the interaction problem. |
| title | Dynamics of the general $Q$-tensor model interacting with a rigid body |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2501.01181 |