Weak solutions of non-isothermal nematic liquid crystal flow in dimension three

For any smooth domain $Omegasubset mathbb{R}^3$, we establish the existence of a global weak solution $(mathbf{u},mathbf{d}, theta)$ to the simplified, non-isothermal Ericksen-Leslie system modeling the hydrodynamic motion of nematic liquid crystals with variable temperature for any initial and boundary data $(mathbf{u}_0, mathbf{d}_0, theta_0)inmathbf{H}times H^1(Omega, mathbb{S}^2)times L^1(Omega)$, with $ mathbf{d}_0(Omega)subsetmathbb{S}_+^2$ (the upper half sphere) and $displaystyleinf_Omega theta_0>0$.