GLOBAL STRONG SOLUTION TO THE DENSITY-DEPENDENT INCOMPRESSIBLE FLOW OF LIQUID CRYSTALS

摘要

The initial-boundary value problem for the density-dependent incompressible flow of liquid crystals is studied in a three-dimensional bounded smooth domain. For the initial density away from vacuum, the existence and uniqueness are established for both the local strong solution with large initial data and the global strong solution with 'small' data. It is also proved that when the strong solution exists, a weak solution with the same data must be equal to the unique strong solution.