On the uniqueness of heat flow of harmonic maps and hydrodynamic flow of nematic liquid crystals

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Regularity and Existence of Global Solutions to the Ericksen–Leslie System in $${\mathbb{R}^2}$$R2 (2013, methodology): “For dimension 2, Lin-Lin-Wang [23] and Lin-Wang [24] have established the existence of a global unique weak solution of (1.”
Global Existence of Weak Solutions of the Nematic Liquid Crystal Flow in Dimension Three (2014, background): “In particular, the existence of global Leray-Hopf type weak solutions to the initial and boundary value problem of (1.1) has only been established recently by Lin-Lin-Wang [15] in dimension two, see also Hong [7] and Xu-Zhang [27] for related works.”
Strong solutions of the compressible nematic liquid crystal flow (2011, background): “When dealing with the incompressible nematic liquid crystal flow, Lin-Lin-Wang [25] and LinWang [23] have established the global existence of a unique ”almost strong” solution2 for the initialboundary value problem in bounded domains in dimension two, see also Hong [14] and Xu-Zhang [38] for some re”