Attractors for Noncompact Nonautonomous Systems Via Energy Equations

Abstract

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.

Department(s)

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)

1078-0947

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2023 American Institute of Mathematical Sciences (AIMS), All rights reserved.

Publication Date

01 Jan 2004

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