Well-posedness and global attractors for liquid crystals on Riemannian manifolds
| dc.creator | Shkoller, Steve | |
| dc.date | 2001-01-24 | |
| dc.date.accessioned | 2026-07-07T04:39:48Z | |
| dc.date.available | 2026-07-07T04:39:48Z | |
| dc.description | We study the coupled Navier-Stokes Ginzburg-Landau model of nematic liquid crystals introduced by F.H. Lin, which is a simplified version of the Ericksen-Leslie system. We generalize the model to compact n-dimensional Riemannian manifolds, and show that the system comes from a variational principle. We present a new simple proof for the local well-posedness of this coupled system without using the higher-order energy law. We then prove that this system is globally well-posed and has compact global attractors when the dimension of the manifold M is two.Finally, we introduce the Lagrangian averaged liquid crystal equations, which arise from averaging the Navier-Stokes fluid motion over small spatial scales in the variational principle. We show that this averaged system is globally well-posed and has compact global attractors even when M is three-dimensional. | |
| dc.identifier | https://arxiv.org/abs/math/0101203 | |
| dc.identifier | http://arxiv.org/abs/math/0101203 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60815 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35Q30, 35Q72 | |
| dc.title | Well-posedness and global attractors for liquid crystals on Riemannian manifolds | |
| dc.type | text |