Periodic Lp estimates by R-boundedness: Applications to the Navier--Stokes equations

General evolution equations in Banach spaces are investigated. Based on an operator-valued version of de Leeuw's transference principle, time-periodic Lp estimates of maximal regularity type are established from R-bounds of the family of solution operators (R-solvers) to the corresponding resolvent problems. With this method, existence of time-periodic solutions to the Navier--Stokes equations is shown for two configurations: in a periodically moving bounded domain and in an exterior domain, subject to prescribed time-periodic forcing and boundary data.

URI

https://oa.tib.eu/renate/handle/123456789/9689
https://doi.org/10.34657/8727

Citation

Eiter, T., Kyed, M., & Shibata, Y. (2022). Periodic Lp estimates by R-boundedness: Applications to the Navier--Stokes equations (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik. https://doi.org//10.20347/WIAS.PREPRINT.2931

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Mathematik
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