Abstract
AbstractGeneral evolution equations in Banach spaces are investigated. Based on an operator-valued version of de Leeuw’s transference principle, time-periodic $\mathrm {L}_{p}$
L
p
estimates of maximal regularity type are carried over 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.
Funder
Toyota Central Research Institute Joint Research Fund
Japan Society for the Promotion of Science London
Weierstraß-Institut für Angewandte Analysis und Stochastik, Leibniz-Institut im Forschungsverbund Berlin e.V.
Publisher
Springer Science and Business Media LLC
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