论文标题
尺寸三的非等温列液晶流的弱解
Weak solutions of non-isothermal nematic liquid crystal flow in dimension three
论文作者
论文摘要
For any smooth domain $Ω\subset \mathbb{R}^3$, we establish the existence of a global weak solution $(\mathbf{u},\mathbf{d}, θ)$ 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 {d} _0（ω）\ subset \ mathbb {s} _+^2 $（上半球）和$ \ displayStyle \ displayStyle \inf_ωθ_0> 0 $。
For any smooth domain $Ω\subset \mathbb{R}^3$, we establish the existence of a global weak solution $(\mathbf{u},\mathbf{d}, θ)$ 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 $(\mathbf{u}_0, \mathbf{d}_0, θ_0)\in\mathbf{H}\times H^1(Ω, \mathbb{S}^2)\times L^1(Ω)$, with $ \mathbf{d}_0(Ω)\subset\mathbb{S}_+^2$ (the upper half sphere) and $\displaystyle\inf_Ωθ_0>0$.
