ABSTRACT

In this paper, we prove the global strong solutions for the Cauchy problem of two-dimensional (2D) incompressible non-isothermal nematic liquid crystal flows, if the initial orientation satisfies a geometric condition. Note that the initial data can be arbitrarily large and the initial density can contain vacuum states. When d is a constant vector and $|d|=1$, we also extend the corresponding result in Wang Y. [Global strong solution to the two dimensional nonhomogeneous incompressible heat conducting Navier–Stokes flows with vacuum. Discrete Contin Dyn Syst B. doi:10.3934/dcdsb.2020099.] to the whole space ${\mathbb{R}}^2$, where the global strong solution of 2D inhomogeneous incompressible heat conducting Navier–Stokes flows is established on bounded domain.

摘要

在本文中，如果初始取向满足几何条件，我们证明了二维（2D）不可压缩非等温向列液晶流的柯西问题的全局强解。请注意，初始数据可以任意大，初始密度可以包含真空状态。当d是一个常数向量并且$|d|=1$，我们还扩展了 Wang Y 中的相应结果。Discrete Contin Dyn Syst B. doi:10.3934/dcdsb.2020099.] 到整个空间${\mathbb{R}}^2$，其中二维非均匀不可压缩导热纳维-斯托克斯流的全局强解建立在有界域上。