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October, 2017 Maximal regularity of the time-periodic Stokes operator on unbounded and bounded domains
Yasunori MAEKAWA, Jonas SAUER
J. Math. Soc. Japan 69(4): 1403-1429 (October, 2017). DOI: 10.2969/jmsj/06941403


We investigate the time-periodic Stokes equations with non-homogeneous divergence data in the whole space, the half space, bent half spaces and bounded domains. The solutions decompose into a well-studied stationary part and a purely periodic part, for which we establish $\mathrm{L}^{p}$ estimates. For the whole space and the half space case we use a reduction of the Stokes equations to $(n-1)$ heat equations. Perturbation and localisation methods yield the result on bent half spaces and bounded domains. A one-to-one correspondence between maximal regularity for the initial value problem and time periodic maximal regularity is proven, providing a short proof for the maximal regularity of the Stokes operator avoiding the notion of $\mathcal{R}$-boundedness. The results are applied to a quasilinear model governing the flow of nematic liquid crystals.


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Yasunori MAEKAWA. Jonas SAUER. "Maximal regularity of the time-periodic Stokes operator on unbounded and bounded domains." J. Math. Soc. Japan 69 (4) 1403 - 1429, October, 2017.


Published: October, 2017
First available in Project Euclid: 25 October 2017

zbMATH: 1380.35044
MathSciNet: MR3715809
Digital Object Identifier: 10.2969/jmsj/06941403

Primary: 35B10 , 76D03
Secondary: 35B45 , 35K59 , 76D07

Keywords: maximal regularity , Stokes operator , time-periodic

Rights: Copyright © 2017 Mathematical Society of Japan


Vol.69 • No. 4 • October, 2017
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