Convergence to equilibrium for smectic-A liquid crystals in 3D domains without constraints for the viscosity
In this paper, we focus on a smectic-A liquid crystal model in 3D domains, and obtain three main results: the proof of an adequate Lojasiewicz-Simon inequality by using an abstract result; the rigorous proof (via a Galerkin approach) of the existence of global intime weak solutions that become stron...
| Autores: | , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2014 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/29571 |
| Acceso en línea: | http://hdl.handle.net/11441/29571 https://doi.org/10.1016/j.na.2014.02.014 |
| Access Level: | acceso abierto |
| Palabra clave: | Liquid crystals Navier-Stokes equations Ginzburg-Landau potential energy dissipation convergence to equilibrium Lojasiewicz-Simon's inequalities |
| Sumario: | In this paper, we focus on a smectic-A liquid crystal model in 3D domains, and obtain three main results: the proof of an adequate Lojasiewicz-Simon inequality by using an abstract result; the rigorous proof (via a Galerkin approach) of the existence of global intime weak solutions that become strong (and unique) in long-time; and its convergence to equilibrium of the whole trajectory as time goes to in nity. Given any regular initial data, the existence of a unique global in-time regular solution (bounded up to in nite time) and the convergence to an equilibrium have been previously proved under the constraint of a su ciently high level of viscosity. Here, all results are obtained without imposing said constraint. |
|---|