| Abstract: |
| We study the Cauchy problem of the Poiseuille flow of full Ericksen-Leslie model for nematic liquid crystals. The model is a coupled system of a parabolic equation for the velocity of fluid and a (quasilinear) wave equation for the director field of liquid crystal molecules. For a particular choice of several physical parameter values, we construct solutions with smooth initial data and finite energy that produce, singularities-blowups of gradients in finite time in both 1D and 2D. We are also able to establish the existence of global weak solutions that are Holder continuous in 1D. |
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