We are concerned with global well-posedness of strong solutions to the Cauchy problem for compressible non-isothermal nematic liquid crystal flows with vacuum as far field density in ${\mathbb{R}}^3$. By using energy method, we establish the global existence and uniqueness of strong solutions provided that the quantity${\Vert {\rho }_0\Vert }_{L^{\infty }}+{\Vert \nabla d_0\Vert }_{L^3}$ is suitably small and the viscosity coefficients verify $3\mu >\lambda$. In particular, the initial density can even have compact support. When $d$ is a constant vector and $\left|d\right|=1$, we also extend partially the corresponding result in Li (2020) where the global small solution of full compressible Navier–Stokes equations was obtained under the condition $2\mathrm{\mu }>\lambda$. To our knowledge, the result in this paper could be viewed as the first one on the global existence of strong solutions to 3D Cauchy problem for compressible non-isothermal nematic liquid crystal flows with vacuum.

我们关注的是对于在真空中具有远至场密度的可压缩非等温向列液晶流的柯西问题的强解的整体适定性。 ${\mathbb{[R}}^3$。通过使用能量方法，我们建立了强解的全局存在性和唯一性${\Vert {\rho }_0\Vert }_{{\mathrm{大号}}^{\infty }}+{\Vert \nabla d_0\Vert }_{{\mathrm{大号}}^3}$ 适当小，粘度系数验证 $3\mu >\lambda$。特别地，初始密度甚至可以具有紧凑的支撑。什么时候$d$ 是一个常数向量， $\left|d\right|=\mathrm{1个}$，我们还部分扩展了Li（2020）中的相应结果，其中在一定条件下获得了完全可压缩Navier–Stokes方程的全局小解 $2\mathrm{\mu }>\lambda$。据我们所知，本文的结果可被视为关于真空可压缩非等温向列液晶流的3D Cauchy问题强解的整体存在的全球性的第一篇论文。