标题： 双维双曲型Ericksen-Leslie系统的Poiseuille流 显示英文标题

标题： Poiseuille flow of hyperbolic Ericksen-Leslie system in dimension two

摘要： 本文研究了全埃里克森- Leslie 系统下的管内泊肃叶层流流动。这是一个可能在有限时间内产生奇点的抛物线-双曲耦合系统。我们将证明能量弱解的整体存在性以及系统的部分正则性。我们首先通过 Ginzburg-Landau 近似和不动点论证构建全局弱有限能量解。然后得到解的增强正则性。与一维空间中的解不同，管内泊肃叶层流流动的能量有限解仍可能在原点形成不连续性。我们表明，在首次可能的爆破时刻，存在收敛到非恒定时间无关（轴对称）谐波映射的爆破序列。 显示英文摘要

摘要： In this paper, we study the Poiseuille laminar flow in a tube for the full Ericksen-Leslie system. It is a parabolic-hyperbolic coupled system which may develop singularity in finite time. We will prove the global existence of energy weak solution, and the partial regularity of solution to system. We first construct global weak finite energy solutions by the Ginzburg- Landau approximation and the fixed-point arguments. Then we obtain the enhanced regularity of solution. Different from the solution in one space dimension, the finite energy solution of Poiseuille laminar flow in a tube may still form a discontinuity at the origin. We show that at the first possible blowup time, there are blowup sequences which converge to a non-constant time-independent (axisymmetric) harmonic map.