The $\mathcal{R}$-boundedness of solution operators for the $Q$-tensor model of nematic liquid crystals
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916781178748928 |
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| author | Barbera, Daniele Murata, Miho |
| author_facet | Barbera, Daniele Murata, Miho |
| contents | In this paper, we consider a resolvent problem arising from the $Q$-tensor model for liquid crystal flows in the half-space. Our purpose is to show the $\mathcal{R}$-boundedness for the solution operator families of the resolvent problem when the resolvent parameter lies near the origin. The definition of the $\mathcal{R}$-solvability implies the uniform boundedness of the operator and, consequently, the resolvent estimates for the linear system. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_05152 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The $\mathcal{R}$-boundedness of solution operators for the $Q$-tensor model of nematic liquid crystals Barbera, Daniele Murata, Miho Analysis of PDEs Mathematical Physics 76A15, 35Q30, 35Q35 In this paper, we consider a resolvent problem arising from the $Q$-tensor model for liquid crystal flows in the half-space. Our purpose is to show the $\mathcal{R}$-boundedness for the solution operator families of the resolvent problem when the resolvent parameter lies near the origin. The definition of the $\mathcal{R}$-solvability implies the uniform boundedness of the operator and, consequently, the resolvent estimates for the linear system. |
| title | The $\mathcal{R}$-boundedness of solution operators for the $Q$-tensor model of nematic liquid crystals |
| topic | Analysis of PDEs Mathematical Physics 76A15, 35Q30, 35Q35 |
| url | https://arxiv.org/abs/2506.05152 |