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

摘要: For any n-dimensional compact Riemannian manifold (M, g) without boundary and another (N, h), the authors establish uniqueness of heat flow harmonic maps from M to N in class C([0, T),W 1,n ). hydrodynamic (u, d) nematic liquid crystals dimensions n = 2 or 3, it is shown that holds for weak solutions provided either (i) 2, u ∈ L ∞ 2 ∩ H 1 , ▿ P 4/3 ▿d ; (ii) C ([0, T), n ), /2 This answers affirmatively question posed by Lin-Lin-Wang. The proofs are very elementary.