Robinson, James C. and Vidal López, Alejandro (2006) Minimal periods of semilinear evolution equations with Lipschitz nonlinearity. Journal of Differential Equations, 220 (2). pp. 396-406. ISSN 0022-0396
Official URL: http://www.sciencedirect.com/science/journal/00220396
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.
|Uncontrolled Keywords:||Period orbits; Minimal period; Semilinear evolution equations; Navier–Stokes equations|
|Subjects:||Sciences > Mathematics > Differential equations|
|Deposited On:||13 Apr 2011 10:37|
|Last Modified:||13 Apr 2011 10:37|
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