Finite time singularity of the nematic liquid crystal flow in dimension three

Abstract

In this paper, we consider the initial and boundary value problem of a simplified nematic liquid crystal flow in dimension three and construct two examples of finite time singularity. The first example is constructed within the class of axisymmetric solutions, while the second example is constructed for any generic initial data $(u_0,d_0)$ that has sufficiently small energy, and $d_0$ has a nontrivial topology

27 pages

References in corpus (3)

• Recent developments of analysis for hydrodynamic flow of nematic liquid crystals
• Global Small Solutions to a Complex Fluid Model in 3D
• On a family of exact solutions to the incompressible liquid crystals in two dimensions

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