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arXiv · 2202.01955

On singularities of Ericksen-Leslie system in dimension three

Tao Huang·Peiyong Wang
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Abstract

In this paper, we consider the initial and boundary value problem of Ericksen-Leslie system modeling nematic liquid crystal flows in dimension three. Two examples of singularity at finite time are constructed. The first example is constructed in a special axisymmetric class with suitable axisymmetric initial and boundary data, while the second example is constructed for an initial data with small energy but nontrivial topology. A counter example of maximum principle to the system is constructed by utilizing the Poiseuille flow in dimension one.

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Tao Huang, Peiyong Wang. 2022-02-04. On singularities of Ericksen-Leslie system in dimension three. https://arxiv.org/abs/2202.01955

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