The recent paper considers the incompressible hydrodynamic flow of biaxial nematic liquid crystal in dimensions N with N = 2 or 3. The unique local solutions are firstly derived for ${\rho }_0\ge 0$ in dimensions 2 and 3. Then the unique global solution is obtained for $0<M_1\le {\rho }_0$ and small initial energy: ${\int }_{\mathrm{\Omega }}({\rho }_0|v_0{|}^2+|\mathrm{\nabla }{n}_0{|}^2+|\mathrm{\nabla }{m}_0{|}^2)\mathrm{d}x$.

中文翻译：

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不可压缩双轴向列液晶流解的存在

最近的论文考虑了N = 2 或 3 维数N的双轴向列液晶的不可压缩流体动力学流动。 首先导出了唯一的局部解${\rho }_0\ge 0$在维度 2 和 3。然后获得唯一的全局解$0<{米}_1\le {\rho }_0$和小的初始能量：${\int }_{\mathrm{\Omega }}({\rho }_0|v_0{|}^2+|\mathrm{\nabla }{n}_0{|}^2+|\mathrm{\nabla }{米}_0{|}^2)\mathrm{d}X$.