%0 Journal Article
%A Robinson, James C.
%A Vidal López, Alejandro
%T Minimal periods of semilinear evolution equations with Lipschitz nonlinearity
%D 2006
%@ 0022-0396
%U https://hdl.handle.net/20.500.14352/49662
%X It is known that any periodic orbit of a Lipschitz ordinary differential equation  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.
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