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

2022/04/24 by Thomas Eiter, Eiter, Thomas, Mads Kyed +3
Engineering · Mathematics · #35B10 #35B45 #35K90 #47J35 #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2204.11290

openalex publication_date 2022/04/24 · openalex created_date 2022/04/28 · openalex updated_date 2026/07/28

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 established from \mathscrR-bounds of the family of solution operators (\mathscrR-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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