WIAS Preprint No. 2931, (2022)

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


  • Eiter, Thomas
    ORCID: 0000-0002-7807-1349
  • Kyed, Mads
    ORCID: 0000-0002-9803-8132
  • Shibata, Yoshihiro

2020 Mathematics Subject Classification

  • 47J35 35K90 35B10 35B45


  • Evolution equations, time-periodic solutions, Lp estimates, Navier--Stokes equations, inhomogeneous boundary data




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.

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