For 3D compressible liquid crystal flows with density-dependent viscosity, global strong solutions exist for large initial density and small director gradient, with no smallness condition on velocity.
Ma, Classical solutions for the compressible liquid crystal flows with nonnegative initial densities, J
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Global strong solution of the 3D compressible liquid crystal flows with density-dependent viscosity and large velocity
For 3D compressible liquid crystal flows with density-dependent viscosity, global strong solutions exist for large initial density and small director gradient, with no smallness condition on velocity.