On the well-posedness for the compressible nematic liquid crystal flow

Abstract

The Cauchy problem for the compressible flow of nematic liquid crystals in dimension ( N ≧ 2) is considered. Employing the Littlewood-Paley theory and Schauder-Tychonoff fixed point theorem, we prove the local well-posedness of the system for large initial data in critical Besov spaces based on the L p framework under the sole natural assumption that the initial density is bounded away from zero.