# American Institute of Mathematical Sciences

December  2012, 32(12): 4171-4182. doi: 10.3934/dcds.2012.32.4171

## On a double penalized Smectic-A model

 1 Dpto. Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Aptdo. 1160, 41080 Sevilla

Received  September 2011 Published  August 2012

In smectic-A liquid crystals, a unity director vector $\boldsymbol{n}$ appear modeling an average preferential direction of the molecules and also the normal vector of the layer configuration. In the E's model [5], the Ginzburg-Landau penalization related to the constraint $|\boldsymbol{n}|=1$ is considered and, assuming the constraint $\nabla\times \boldsymbol{n}=0$, $\boldsymbol{n}$ is replaced by the so-called layer variable $\varphi$ such that $\boldsymbol{n}=\nabla\varphi$.
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 $\boldsymbol{n}$. 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.
Citation: Blanca Climent-Ezquerra, Francisco Guillén-González. On a double penalized Smectic-A model. Discrete & Continuous Dynamical Systems - A, 2012, 32 (12) : 4171-4182. doi: 10.3934/dcds.2012.32.4171
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