Mathematical analysis demonstrates global existence, uniqueness, and algebraic decay rates for 3D liquid crystal flows with vacuum, indicating stability under viscosity-dependent conditions.
We consider the Cauchy problem of non-isothermal inhomogeneous nematic liquid crystal flows in [Formula: see text]. Based on the energy method, we derive the global existence and uniqueness of strong solutions with both interior and far field vacuum when [Formula: see text] is sufficiently small. In particular, the smallness depends only on the viscosity coefficient. Moreover, we also obtain algebraic decay-in-time rates of the solution.
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Zhang et al. (2026) studied this question.
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