Abstract
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.
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