Existence of solutions to incompressible biaxial nematic liquid crystals flows

Authors：Gong, Weihua; Lin, Junyu^*

Source：APPLICABLE ANALYSIS, 2022, 101(16): 5872-5905.

DOI：10.1080/00036811.2021.1909723

• Liquid crystal
• biaxial nematic
• incompressible flow
• global solution

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 rho(0)>= 0 in dimensions 2 and 3. Then the unique global solution is obtained for 0 < M-1 <= rho(0) and small initial energy: integral(Omega) (rho(0)|v(0)|(2) + |del n(0)|(2) + |del m(0)|(2)) dx.