Twisted solutions to a simplified Ericksen-Leslie equation (Q1729853)

The main purpose of the present paper is to construct a global solution for a class of simplified Ericksen-Leslie systems. The main idea is to use a suitable \(m\)-equivariant ansatz, which ensures that the incompressibility condition in the system is fulfilled. These solutions become singular at all points on the \(x_3\)-axis and escape into third dimension exponentially while \(t\) goes to \(\infty\). An optimal blow up rate is also obtained.