Abstract
We consider the dynamics of spatially periodic nematic liquid crystal flows in the whole space and prove existence and uniqueness of local-in-time strong solutions using maximal L p-regularity of the periodic Laplace and Stokes operators and a local-intime existence theorem for quasilinear parabolic equations à la Clément-Li (1993). Maximal regularity of the Laplace and the Stokes operator is obtained using an extrapolation theorem on the locally compact abelian group \(G: = \mathbb{R}^{n - 1} \times \mathbb{R}/L\mathbb{Z}\) to obtain an R-bound for the resolvent estimate. Then, Weis’ theorem connecting R-boundedness of the resolvent with maximal L p regularity of a sectorial operator applies.
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The author has been supported by the International Research Training Group 1529.
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Sauer, J. Maximal regularity of the spatially periodic stokes operator and application to nematic liquid crystal flows. Czech Math J 66, 41–55 (2016). https://doi.org/10.1007/s10587-016-0237-2
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DOI: https://doi.org/10.1007/s10587-016-0237-2
Keywords
- Stokes operator
- spatially periodic problem
- maximal L p regularity
- nematic liquid crystal flow
- quasilinear parabolic equations