Regularity and Existence of Global Solutions to the Ericksen–Leslie System in $${\mathbb{R}^2}$$R2

By Jinrui Huang, F. Lin, Changyou Wang. 2013

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In this paper, we first establish the regularity theorem for suitable weak solutions to the Ericksen–Leslie system in $${\mathbb{R}^2}$$R2. Building on such a regularity, we then establish the existence of a global weak solution to the Ericksen–Leslie system in $${\mathbb{R}^2}$$R2 for any initial data in the energy space, under the physical constraints on the Leslie coefficients ensuring the dissipation of energy of the system, which is smooth away from at most finitely many times. This extends earlier works by Lin et al. (Arch Ration Mech Anal 197:297–336, 2010) on a simplified nematic liquid crystal flow to the general Ericksen–Leslie system.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ce25d3951c1f16cdf799129f9c0cab2b4a4faf3d