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

Abstract

For any smooth domain $\Omega \subset {\mathbb{R}}^3$, 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 $({\mathbf{u}}_0,{\mathbf{d}}_0,{\theta }_0)\in \mathbf{H}\times H^1(\Omega ,{\mathbb{S}}^2)\times L^1(\Omega )$, with ${\mathbf{d}}_0(\Omega )\subset {\mathbb{S}}_{+}^2$ (the upper half sphere) and $\underset{\Omega }{\inf }{\theta }_0>0$.

23 pages

References in corpus (1)

• Recent developments of analysis for hydrodynamic flow of nematic liquid crystals