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

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.

preprint2012arXivOpen access
Hongjie DongZhen Lei
math.AP
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Open access2 authors1 topic
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Hongjie DongZhen Lei

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