Moise, Ioana; Rosa, Ricardo; Wang, Xiaoming Attractors for non-compact semigroups via energy equations. (English) Zbl 0914.35023 Nonlinearity 11, No. 5, 1369-1393 (1998). Summary: The energy-equation approach used to prove the existence of the global attractor by establishing the so-called asymptotic compactness property of the semigroup is considered, and a general formulation that can handle a numher of weakly damped hyperbolic equations and parabolic equations on either bounded or unbounded spatial domains is presented. As examples, three specific and physically relevant problems we considered, namely the flows of a second-grade fluid, the flows of a Newtonian fluid in an infinite channel past an obstacle, and a weakly damped, forced Korteweg-de Vries equation on the whole line. Cited in 1 ReviewCited in 80 Documents MSC: 35B40 Asymptotic behavior of solutions to PDEs 35Q30 Navier-Stokes equations 37C70 Attractors and repellers of smooth dynamical systems and their topological structure 35Q53 KdV equations (Korteweg-de Vries equations) 76A05 Non-Newtonian fluids 76D05 Navier-Stokes equations for incompressible viscous fluids Keywords:asymptotic compactness property; bounded or unbounded spatial domains PDFBibTeX XMLCite \textit{I. Moise} et al., Nonlinearity 11, No. 5, 1369--1393 (1998; Zbl 0914.35023) Full Text: DOI Link