Well-posedness of Entropy-Bounded Solutions to 3D Compressible Nematic Liquid Crystal Flows with Far Field Vacuum

Abstract

The kinetic behavior of the physical entropy of viscous and heat-conductive fluids is an important and challenging problem, since the entropy equation possesses high degeneracy and singularity in the vacuum region. This article presents a conclusion that for the heat-conductive compressible nematic liquid system, the strong solution to the Cauchy problem is uniformly bounded in entropy and the \(L^{2}\) regularities of the velocity and temperature can be preserved, provided the initial density vanishes in the far field is less than \(O \left( \frac{1}{|x |^{2}}\right) \), which improved the previous work [18]. The proof relies on the singular weighted energy method and a modified De Giorgi type iterative technique.