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<p>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.</p>

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Poiseuille flow of hyperbolic Ericksen-Leslie system in dimension two

  • 期刊论文

  • 发表日期：

    2026年1月12日

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  • Geng Chen,
  • Tao Huang,
  • Xiang Xu,
  • Qingtian Zhang

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.