Global low-energy weak solution and large-time behavior for the compressible flow of liquid crystals

Abstract

In this paper, we consider the weak solution of the simplified Ericksen–Leslie system modeling compressible nematic liquid crystal flows in R3. When the initial data are of small energy and initial density is positive and essentially bounded, we prove the existence of a global weak solution in R3. The large-time behavior of a global weak solution is also established.