Minimal periods of semilinear evolution equations with Lipschitz nonlinearity

James C. Robinson*, Alejandro Vidal-López

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


It is known that any periodic orbit of a Lipschitz ordinary differential equation ẋ = f(x) must have period at least 2π/L, where L is the Lipschitz constant of f. In this paper, we prove a similar result for the semilinear evolution equation du/dt = -Au + f(u): for each α with 0 ≤ α ≤ 1/2 there exists a constant Kα such that if L is the Lipschitz constant of f as a map from D(Aα) into H then any periodic orbit has period at least KαL-1/(1-α). As a concrete application we recover a result of Kukavica giving a lower bound on the period for the 2d Navier-Stokes equations with periodic boundary conditions.

Original languageEnglish
Pages (from-to)396-406
Number of pages11
JournalJournal of Differential Equations
Issue number2
Publication statusPublished - 15 Jan 2006
Externally publishedYes


  • Minimal period
  • Navier-Stokes equations
  • Period orbits
  • Semilinear evolution equations

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