Global existence of low‐energy weak solutions to the compressible nematic liquid crystal flows

We consider the compressible nematic liquid crystal flows with no‐slip boundary condition for velocity and Neumann boundary condition for macroscopic molecular orientation in a half‐space . We prove the global existence of low‐energy weak solutions to the compressible nematic liquid crystal flows when the discontinuous initial data close to a static equilibrium by using Hoff's method. Moreover, we also show that the density is uniformly bounded, the velocity and macroscopic molecular orientation are Hölder continuous in the half‐space, and Lipschitz continuous on the boundary of the half‐space when the initial data is discontinuous.