Attractors for Noncompact Nonautonomous Systems Via Energy Equations
An extension to the nonautonomous case of the energy equation method for proving the existence of attractors for noncompact systems is presented. a suitable generalization of the asymptotic compactness property to the nonautonomous case, termed uniform asymptotic compactness, is given, and conditions on the energy equation associated with an abstract class of equations that assure the uniform asymptotic compactness are obtained. This general formulation is then applied to a nonautonomous Navier-Stokes system on an infinite channel past an obstacle, with time-dependent forcing and boundary conditions, and to a nonautonomous, weakly damped, forced Korteweg-de Vries equation on the real line.
I. Moise et al., "Attractors for Noncompact Nonautonomous Systems Via Energy Equations," Discrete and Continuous Dynamical Systems, vol. 10, no. 1 thru 2, pp. 473 - 496, American Institute of Mathematical Sciences (AIMS), Jan 2004.
The definitive version is available at https://doi.org/10.3934/dcds.2004.10.473
Mathematics and Statistics
Keywords and Phrases
Energy Equation; Korteweg-De-Vries Equation; Navier-Stokes Equations; Nonautonomous Equations; Uniform Asymptotic Compactness; Uniform Attractors
International Standard Serial Number (ISSN)
Article - Journal
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01 Jan 2004