On The Number Of Singular Points Of Weak Suitable Solutions To The Systems Modeling The Flow Of Incompressible Liquid Crystals

In this paper, we consider the Hoder continuity of a suitable weak solution to a simplified system of incompressible nematic liquid crystals in the space-time cylinder QT=Ω×(O,T). We get a criterion of local Holder continuity for the solution and give a estimation on the number of singular points of it.In Chapter1, we deduce an energy inequality for the system if the solution exists, and give the definition of suitable weak solution to the system.In Chapter3, we use a method called blow-up procedure which makes a series of scal-ing. By using the energy inequality, we get the strong convergence of the function series and prove a condition for the Holder continuity of the suitable weak solution (v, d).Chapter4is based on the conclusion of Chapter3. For a fixed t∈(0, T), let∑(t) be the set of singular points for the weak suitable solution at time t. Letω(?)Ω be an open set. We obtain an upper bound for the number of points of the set∑∩ω.