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Attractors for noncompact nonautonomous systems via energy equations. (English) Zbl 1060.35023
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.

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
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