Existence of solutions to incompressible biaxial nematic liquid crystals flows. Issue 16 (2nd November 2022) - Gong, Weihua; Lin, Junyu
Abstract : The recent paper considers the incompressible hydrodynamic flow of biaxial nematic liquid crystal in dimensions N with N  = 2 or 3. The unique local solutions are firstly derived for ρ 0 ≥ 0 in dimensions 2 and 3. Then the unique global solution is obtained for 0 < M 1 ≤ ρ 0 and small initial energy: ∫ Ω ( ρ 0 | v 0 | 2 + | ∇ n 0 | 2 + | ∇ m 0 | 2 ) d x .