On a family of exact solutions to the incompressible liquid crystals in two dimensions

Abstract

In this paper we construct a family of exact strong solutions to the two-dimensional incompressible liquid crystal equations with finite energy. The initial velocity is chosen to be rotationally symmetric and the image of the initial orientation of the liquid crystal is a non-trivial curve on the unit sphere. It turns out that this family of initial data evolves globally in time by liquid crystal flow and may shrink to a single point as time goes to infinity.

arXiv comment9 pages, submitted

References in corpus (1)

• Well-posedness for the heat flow of harmonic maps and the liquid crystals flow with rough initial data

Cited by in corpus (4)

• Finite time singularity of the nematic liquid crystal flow in dimension three
• Remarks of Global Wellposedness of Liquid Crystal Flows and Heat Flows of Harmonic Maps in Two Dimensions
• Nonexistence of smooth solutions for the general compressible Ericksen -- Leslie equations in three dimensions
• Nonuniqueness of nematic liquid crystal flows in dimension three