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On the temporal decay of solutions to the two‐dimensional nematic liquid crystal flows
Author(s) -
Liu Qiao
Publication year - 2016
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201400313
Subject(s) - liquid crystal , norm (philosophy) , exponential decay , mathematics , energy method , energy (signal processing) , mathematical analysis , physics , condensed matter physics , quantum mechanics , statistics , law , political science
We consider the temporal decay estimates for weak solutions to the two‐dimensional nematic liquid crystal flows, and we show that the energy norm of a global weak solution has non‐uniform decay∥ u ( t ) ∥ L 2 + ∥ ∇ d ( t ) ∥ L 2 → 0 ast → ∞ , under suitable conditions on the initial data. We also show the exact rate of the decay (uniform decay) of the energy norm of the global weak solution.