论文标题
在3D有界结构域中的可压缩列液晶流动的全球强溶液具有较大的振荡和真空的真空
Global existence of strong solutions with large oscillations and vacuum to the compressible nematic liquid crystal flows in 3D bounded domains
论文作者
论文摘要
我们研究了在三维（3D）有界结构域中可压缩的列液晶体流，具有速度和Neumann边界条件的滑动边界条件的方向场。通过基于有效的粘性通量和涡度应用分段 - 估计的方法和精致的分析，只要最初的总能量很小。我们的结果是延伸了黄 - 旺（J.微分方程252：2222-2265，2012）和li-xu-zhang（J.Math。FluidMech。20：2105-2145，2018），在其中三个维度和3D Cauchy问题的全球强大解决方案中，当地强大的解决方案在其中建立了3D Cauchy问题。此外，它还表明，如果初始总能量足够小，就不会发生Huang-Wang-Wen（Arch。Mech。204：285-311，2012）获得的局部强溶液的爆炸机制。
We investigate compressible nematic liquid crystal flows in three-dimensional (3D) bounded domains with slip boundary condition for velocity and Neumann boundary condition for orientation field. By applying piecewise-estimate method and delicate analysis based on the effective viscous flux and vorticity, we derive the global existence and uniqueness of strong solutions provided that the initial total energy is suitably small. Our result is an extension of the works of Huang-Wang-Wen (J. Differential Equations 252: 2222-2265, 2012) and Li-Xu-Zhang (J. Math. Fluid Mech. 20: 2105-2145, 2018), where the local strong solutions in three dimensions and the global strong solutions for 3D Cauchy problem were established, respectively. Moreover, it also shows that blow up mechanism for local strong solutions obtained by Huang-Wang-Wen (Arch. Ration. Mech. Anal. 204: 285-311, 2012) cannot occur if the initial total energy is sufficiently small.
