ABSTRACT In this paper, we investigate the Cauchy problem for the incompressible inhomogeneous nematic liquid crystal flows in with initial data in some critical Besov spaces. Under the assumptions that initial density is close to the equilibrium state and the smallness on the initial direction field and nonlinear smallness on the linearized velocity, we obtain the global existence of solutions by fully using the Fourier localization technique and the advantage of weighted function generated by heat kernel. The meanings of this kind of initial data are that we can provide an example of large highly oscillating data satisfying that nonlinear smallness assumption, despite each component of the initial data could be arbitrarily large.

中文翻译：

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关于不可压缩非均匀向列液晶流的一些大的全局解

摘要 在本文中，我们研究了不可压缩非均匀向列液晶在某些关键 Besov 空间中的初始数据流入的柯西问题。在初始密度接近平衡态、初始方向场较小、线速度非线性较小的假设下，充分利用傅里叶局部化技术和由下式产生的加权函数的优点，得到解的全局存在性。热核。这种初始数据的意义在于我们可以提供一个满足非线性小假设的大高度振荡数据的例子，尽管初始数据的每个分量都可以是任意大的。