Impacto
Downloads
Downloads per month over past year
Robinson, James C. and Vidal López, Alejandro (2006) Minimal periods of semilinear evolution equations with Lipschitz nonlinearity. Journal of Differential Equations, 220 (2). pp. 396406. ISSN 00220396

PDF
169kB 
Official URL: http://www.sciencedirect.com/science/journal/00220396
Abstract
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 KαL1/(1α). 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.
Item Type:  Article 

Uncontrolled Keywords:  Period orbits; Minimal period; Semilinear evolution equations; Navier–Stokes equations 
Subjects:  Sciences > Mathematics > Differential equations 
ID Code:  12584 
Deposited On:  13 Apr 2011 08:37 
Last Modified:  12 Dec 2018 15:07 
Origin of downloads
Repository Staff Only: item control page