Global Existence And Indivable Limit Of Weak Solution Of Compressible Liquid Crystal Equations

The present thesis is concerned with some analysis on compressible liquid crystals system. The main results are seperated into two parts:one is the existence of compress-ible liquid crystals, and the other is about the incompressible limit to the compressible liquid crystals system. These two parts are considered both on whole space RN, N=2,3and bounded domain of RN. The thesis is divided into three chapters.In chapter1, we simply give the construction of liquid crystals model, then introduce the background and main results of this thesis.In chapter2, we prove the global existence of weak solutions to liquid crystals system. We considered the existence on both whole space and bounded domain. On the whole space case, by splitting on p, u, we can get similar results as bounded domain case.In chapter3, we concerned the incompressible limit of compressible liquid crystals sys-tem. In this part, we mainly use the anlysis on spectral of operator, also by virtue of splitting methods similar to chapter2, we obtain some explicit estimations.