Moise, Ioana; Rosa, Ricardo; Wang, Xiaoming Attractors for noncompact nonautonomous systems via energy equations. (English) Zbl 1060.35023 Discrete Contin. Dyn. Syst. 10, No. 1-2, 473-496 (2004). The authors present an extension to the nonautonomous case of the energy equation for proving the existence of attractors for noncompact systems. To this end they generalize asymptotic compactness property and apply the extended theory 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. Reviewer: Messoud A. Efendiev (Berlin) Cited in 47 Documents MSC: 35B41 Attractors 35B40 Asymptotic behavior of solutions to PDEs 35Q30 Navier-Stokes equations 37L30 Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems 35Q53 KdV equations (Korteweg-de Vries equations) 37B25 Stability of topological dynamical systems 76D05 Navier-Stokes equations for incompressible viscous fluids Keywords:nonautonomous Navier-Stokes system; infinite channel past an obstacle; time-dependent forcing; weakly damped Korteweg-de Vries equation; asymptotic compactness PDFBibTeX XMLCite \textit{I. Moise} et al., Discrete Contin. Dyn. Syst. 10, No. 1--2, 473--496 (2004; Zbl 1060.35023) Full Text: DOI