Global strong solutions to compressible non‐isothermal nematic liquid crystal flows with vacuum at infinity in R3$\mathbb {R}^3$

Abstract We consider the Cauchy problem for the compressible non‐isothermal nematic liquid crystal equations in . The existence of global strong solutions is established when the initial mass of the flow and the ‐norm of the spatial derivative of the initial macroscopic average of the nematic liquid crystal orientation field are suitably small. The results show that the strong solution may have large oscillations and can contain vacuum states.