仅具有界密度的非齐次Ericksen-Leslie方程组的整体可解性
Global Solvability of the Inhomogeneous Ericksen-Leslie System with only Bounded Density
摘要：
埃里克森和莱斯利建立了一个理论来模拟液晶的流动。本文研究了他们系统的一个简化形式的柯西问题，它保留了原系统的大部分性质。我们考虑密度依赖的情况下，我们建立了小的初始数据在整个空间的整体存在性的解决方案。初始密度只需要有界且远离真空，而初始速度属于某个临界Besov空间。在初速度具有更强的正则性的条件下，我们还证明了这些解是唯一的。
英文摘要：
Ericksen and Leslie established a theory to model the flow of nematic liquid crystals. This paper is devoted to the Cauchy Problem of a simplified version of their system, which retains most of the properties of the original one. We consider the density-dependent case and we establish the global existence of solutions in the whole space for small initial data. The initial density only has to be bounded and kept far from vacuum, while the initial velocity belongs to some critical Besov Space. Under a little bit more regularity for the initial velocity, we prove also that those solutions are unique.
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