Global solution to the incompressible flow of liquid crystals

Global Solution to the Three-Dimensional Compressible Flow of Liquid Crystals

The equations for the three-dimensional incompressible flow of liquid crystals are considered in a smooth bounded domain. The existence and uniqueness of the global strong solution with small initial data are established. It is also proved that when the strong solution exists, all the global weak solutions constructed in [16] must be equal to the unique strong solution.

Global Strong Solution to the Density-dependent Incompressible Viscoelastic Fluids

The existence and uniqueness of the global strong solution with small initial data to the three-dimensional density-dependent incompressible viscoelastic fluids is established. The local existence and uniqueness of the global strong solution with small initial data to the three-dimensional compressible viscoelastic fluids is also obtained. A new method is developed to estimate the solution with...

Global Weak Solutions to the Equations of Compressible Flow of Nematic Liquid Crystals in Two Dimensions

We consider weak solutions to a simplified Ericksen-Leslie system of two-dimensional compressible flow of nematic liquid crystals. An initialboundary value problem is first studied in a bounded domain. By developing new techniques and estimates to overcome the difficulties induced by the supercritical nonlinearity |∇d|d in the equations of angular momentum on the direction field, and adapting t...

The Solution of Three Dimensional Incompressible Potential Flow Through Rectangular Ducts

The Solution of Laminar Incompressible Flow Equation with Free Surfaces in Curvilinear Coordinates

In this paper a novel numerical approach is presented for solving the transient incompressible fluid flow problems with free surfaces in generalized two-dimensional curvilinear coordinate systems. Solution algorithm is a combination of implicit real-time steps and explicit pseudo-time steps. Governing fluid flow equations are discretized using a collocated finite-volume mesh. Convective terms a...