Local and global existence for the Ericksen-Leslie problem in unbounded domains
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917778833801216 |
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| author | Barbera, Daniele Georgiev, Vladimir |
| author_facet | Barbera, Daniele Georgiev, Vladimir |
| contents | The work deals with the Ericksen-Leslie model for nematic liquid crystals on the whole space, the half-space and on exterior domains with smooth boundary. The crystal orientation is described by a unit vector that is a small perturbation of a fixed constant vector. We prove, through a combination of energy method with dispersive a priori estimates, a local existence and a global existence for small initial data by a contraction argument asking low regularity assumptions on the initial condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_08193 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Local and global existence for the Ericksen-Leslie problem in unbounded domains Barbera, Daniele Georgiev, Vladimir Analysis of PDEs 76A15, 35Q30, 35Q35 The work deals with the Ericksen-Leslie model for nematic liquid crystals on the whole space, the half-space and on exterior domains with smooth boundary. The crystal orientation is described by a unit vector that is a small perturbation of a fixed constant vector. We prove, through a combination of energy method with dispersive a priori estimates, a local existence and a global existence for small initial data by a contraction argument asking low regularity assumptions on the initial condition. |
| title | Local and global existence for the Ericksen-Leslie problem in unbounded domains |
| topic | Analysis of PDEs 76A15, 35Q30, 35Q35 |
| url | https://arxiv.org/abs/2401.08193 |