On a double penalized smectic-A model
In smectic-A liquid crystals a unity director vector n appear, modeling an average preferential direction of the molecules and also the normal vector of the layer configuration. In the E’s model [5] W. E. Nonlinear Continuum Theory of Smectic-A Liquid Crystals, Arch. Rat. Mech. Anal., 137, 2 (2010),...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2012 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/40252 |
| Acceso en línea: | http://hdl.handle.net/11441/40252 https://doi.org/10.3934/dcds.2012.32.4171 |
| Access Level: | acceso abierto |
| Palabra clave: | Smectic-A liquid crystals Navier-Stokes equations Cahn-Hilliard system coupled non-linear parabolic system convergence to equilibrium |
| Sumario: | In smectic-A liquid crystals a unity director vector n appear, modeling an average preferential direction of the molecules and also the normal vector of the layer configuration. In the E’s model [5] W. E. Nonlinear Continuum Theory of Smectic-A Liquid Crystals, Arch. Rat. Mech. Anal., 137, 2 (2010), 1473-1493, the Ginzburg-Landau penalization related to the constraint |n| = 1 is considered and, assuming the constraint ∇ × n = 0, n is replaced by the so-called layer variable ϕ such that n = ∇ϕ. In this paper, a double penalized problem is introduced related to a smectic-A liquid crystal flows, considering a Cahn-Hilliard system to model the behavior of n. Then, the issue of the global in time behavior of solutions is attacked, including the proof of the convergence of the whole trajectory towards a unique equilibrium state. |
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