稳态Q-tensor液晶流的Liouville定理

研究了三维空间中稳态Q-tensor液晶流模型，并用试探函数方法证明了当速度场u\in L^{\frac{\mathrm{9}}{\mathrm{2}},\mathrm{\infty }}({\mathrm{R}}^{\mathrm{3}})?\stackrel{·}{H^{\mathrm{1}}}({\mathrm{R}}^{\mathrm{3}})，液晶的张量型序参量\mathit{Q}\in H^{\mathrm{2}}({\mathrm{R}}^{\mathrm{3}})时，该稳态系统只有零平凡解。

Liouville theorem for steady Q-tensor system of liquid crystal

We study the Liouville theorem for steady Q-tensor system of liquid crystal in R³. Assuming that u\in L^{\frac{\mathrm{9}}{\mathrm{2}},\mathrm{\infty }}({\mathrm{R}}^{\mathrm{3}})?\stackrel{·}{H^{\mathrm{1}}}({\mathrm{R}}^{\mathrm{3}}) and \mathit{Q}\in H^{\mathrm{2}}({\mathrm{R}}^{\mathrm{3}}), we show that the steady system admits only trivial solution u=0, Q =0.