Periodic
Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications(2023)
Abstract
General evolution equations in Banach spaces are investigated. Based on an operator-valued version of de Leeuw’s transference principle, time-periodic 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.
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Key words
Evolution equations,Time-periodic solutions,Lp estimates,Navier-Stokes equations,Inhomogeneous boundary data,47J35,35K90,35B10,35B45
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