  In this paper, we investigate the Beris-Edwards system for both biaxial and
uniaxial $Q$-tensors with a general Landau-de Gennes energy density depending
on four non-zero elastic constants. We prove existence of the strong solution
of the Beris-Edwards system for uniaxial $Q$-tensors up to a maximal time.
Furthermore, we prove that the strong solutions of the Beris-Edwards system for
biaxial $Q$-tensors converge smoothly to the solution of the Beris-Edwards
system for uniaxial $Q$-tensors up to its maximal existence time.
