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<p>In this paper, we focus on the global well-posedness and dynamical stability of the general Ericksen-Leslie system induced by external magnetic fields. We first establish the global existence of a strong solution with planar ansatz for director field, and then study the large time behavior of such a solution, where the equilibrium is related to the elliptic sine-Gordon problem. Finally, the possible threshold for the Freedericksz transition is found with certain constrains. The Leslie tensor and the stretching effect are considered.</p>

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Global Well-posedness and possible Freedericksz transition of the general Ericksen-Leslie system in two dimensional bounded domains

  • 期刊论文

  • 发表日期：

    2025年12月22日

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  • Jinrui Huang,
  • Junyu Lin

摘要

In this paper, we focus on the global well-posedness and dynamical stability of the general Ericksen-Leslie system induced by external magnetic fields. We first establish the global existence of a strong solution with planar ansatz for director field, and then study the large time behavior of such a solution, where the equilibrium is related to the elliptic sine-Gordon problem. Finally, the possible threshold for the Freedericksz transition is found with certain constrains. The Leslie tensor and the stretching effect are considered.