The analysis of harmonic maps and their heat flows

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Global Existence of Weak Solutions of the Nematic Liquid Crystal Flow in Dimension Three (2014, methodology): “Applying the duality between the Hardy space H1(R3) and the BMO space BMO(R(3)) (see [4] [6] or [20]), we then obtain”
Well-posedness for the heat flow of harmonic maps and the liquid crystal flow with rough initial data (2010, background): “In a very recent paper, Lin-Lin-Wang [15] proved, among other results, that for any (u0, d0) ∈ L2(Ω,R2) ×H1(Ω, S2) with ∇ · u0 = 0, there is a global Leray-Hopf type weak solution (u, d) to (1.7)-(1.9) and (1.10) that is smooth away from at most finitely many singular times.”
A Bernstein problem for special Lagrangian equations in exterior domains (2017, background): “The possible changing planes can be in fact ﬁxed by Allard-Almgren through their uniqueness of tangent cones [1]; see also Simon [23], Lin-Wang [20].”
Strong solutions of the compressible nematic liquid crystal flow (2011, background): “[24]) that there exists d0 ∈ H3(R3, S2) such that d0 ≡ n0 outside BR 2 for some constant n0 ∈ S2 and lim R↑∞ ∥”