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arXiv · 1709.06384

Nematic Liquid Crystals in Lipschitz domains

Anupam Pal Choudhury·Amru Hussein·Patrick Tolksdorf
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Abstract

We consider the simplified Ericksen-Leslie model in three dimensional bounded Lipschitz domains. Applying a semilinear approach, we prove local and global well-posedness (assuming a smallness condition on the initial data) in critical spaces for initial data in $L^3_{\sigma}$ for the fluid and $W^{1,3}$ for the director field. The analysis of such models, so far, has been restricted to domains with smooth boundaries.

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Anupam Pal Choudhury, Amru Hussein, Patrick Tolksdorf. 2017-09-19. Nematic Liquid Crystals in Lipschitz domains. https://doi.org/10.1137/17m1160975

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