Global existence for a class of large solution to the three-dimensional isentropic compressible nematic liquid crystal flows

This paper concerns the Cauchy problem for the three-dimensional isentropic compressible nematic liquid crystal flows. It is shown that the unique classical solution to the Cauchy problem for this system with large initial energy and vacuum exists globally in time provided the adiabatic exponent γ is sufficiently close to 1 and the far-field density ρ∞ is either vacuum or near vacuum. To the best of our knowledge, this is the first result on the global existence of large-energy solutions with vacuum to the three-dimensional isentropic compressible nematic liquid crystal flows for both vacuum and non-vacuum far-field constant states, which generalizes the results of [Li, Xu, and Zhang, J. Math. Fluid Mech. 20, 2105–2145 (2018)] where the solutions with small energy but possibly large oscillations are established.