标题： 非均匀埃里克森-莱斯利系统的全局可解性仅具有有界密度 显示英文标题

标题： 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向列相液晶的流动。 本文致力于他们系统的一个简化版本的柯西问题，该版本保留了原系统的大部分性质。 我们考虑密度依赖的情况，并在全空间中为小初始数据建立了解的全局存在性。 初始密度只需有界并远离真空，而初始速度属于某个临界贝索空间。 在初始速度具有稍微高一点的正则性条件下，我们还证明了这些解是唯一的。 显示英文摘要

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.