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On a double penalized Smectic-A model

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  • 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.
    Mathematics Subject Classification: Primary: 76A15; Secondary: 35A35, 35Q35, 35K30, 76D05, 76A10, 76D03.


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