Global regularity to the 2D non-isothermal inhomogeneous nematic liquid crystal flows

Abstract

ABSTRACT In this paper, we prove the global strong solutions for the Cauchy problem of two-dimensional (2D) incompressible non-isothermal nematic liquid crystal flows, if the initial orientation satisfies a geometric condition. Note that the initial data can be arbitrarily large and the initial density can contain vacuum states. When d is a constant vector and , we also extend the corresponding result in Wang Y. [Global strong solution to the two dimensional nonhomogeneous incompressible heat conducting Navier–Stokes flows with vacuum. Discrete Contin Dyn Syst B. doi:10.3934/dcdsb.2020099.] to the whole space , where the global strong solution of 2D inhomogeneous incompressible heat conducting Navier–Stokes flows is established on bounded domain.