Dynamic theory for incompressible smectic-A liquid crystals: existence and regularity
The author studies the following evolution system that models fluids which are under influence of internal molecule layers, that is: \[ \begin{aligned} & \rho_t+\nabla\cdot (\rho v)=0,\\ & \rho\dot v+\nabla(-pI+\sigma^e+\sigma^d),\\ & \dot\varphi = \lambda(\nabla\cdot (\xi \nabla \varphi)-K\Delta^2\varphi),\end{aligned} \] where \(\rho:\Omega\times [0,\infty)\to\mathbb{R}\) is the density of materials, \(p\) is the scalar function describing the fluid pressure, \(v:\Omega\times [0,\infty)\to\mathbb{R}^3(\mathbb{R}^2)\) is the flow velocity, and \(\varphi:\Omega\times [0,\infty)\to\mathbb{R}\) is the layer variable. Here \(\Omega\) is a bounded domain in \(\mathbb{R}^3(\mathbb{R}^2)\). The author proves existence of global weak solutions. Moreover, he discusses some regularity and stability results.
scientific article; zbMATH DE number 1492660