Global strong solutions for the incompressible nematic liquid crystal flows with density-dependent viscosity coefficient

This paper is concerned with an initial-boundary value problem of the incompressible nematic liquid crystal flows with density-dependent viscosity in a smooth bounded domain Ω⊂R3. The global well-posedness of strong solutions with large oscillations is established in vacuum, provided ‖∇u0‖L2+‖Δd0‖L2 is suitably small with arbitrary large initial density, which extended the local strong solution by Gao et al. [12] to be a global one.