Abstract
We consider a complex fluid modeling nematic liquid crystal flows, which is described by a system coupling Navier-Stokes equations with a parabolic Q-tensor system. We first prove the global existence of weak solutions in dimension three. Furthermore, the global well-posedness of strong solutions is studied with sufficiently large viscosity of fluid. Finally, we show a continuous dependence result on the initial data which directly yields the weak-strong uniqueness of solutions.
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Huang, J., Ding, S. Global well-posedness for the dynamical Q-tensor model of liquid crystals. Sci. China Math. 58, 1349–1366 (2015). https://doi.org/10.1007/s11425-015-4990-8
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DOI: https://doi.org/10.1007/s11425-015-4990-8