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Decay of the nematic liquid crystal system. (English) Zbl 1339.35218

Summary: In this paper, we study the time-decay rates of the solution to the Cauchy problem for a nematic liquid crystals system via a refined pure energy method. In particular, the optimal decay rates of the higher-order spatial derivatives of the solution are obtained. The \(\dot{H}^{-s}(0\leq s\leq \frac{1}{2})\) negative Sobolev norms are shown to be preserved along time evolution and enhance the decay rates.

MSC:

35Q30 Navier-Stokes equations
76N15 Gas dynamics (general theory)
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
82C40 Kinetic theory of gases in time-dependent statistical mechanics
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