Convergent families of approximate inertial manifolds

zbMath0836.35063MaRDI QIDQ1900629

Arnaud Debussche, Roger M. Temam

Publication date: 29 April 1996

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

zbMATH Keywords

approximate inertial manifoldsLyapunov-Perron construction

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Initial value problems for linear higher-order PDEs (35G10) Higher-order parabolic equations (35K25) Equations in function spaces; evolution equations (58D25)

Related Items (16)

A convergent family of approximate inertial manifolds ⋮ Approximation of exponential order of the attractor of a turbulent flow ⋮ Inertial manifolds with delay ⋮ On computing the long-time solution of the two-dimensional Navier-Stokes equations ⋮ The nonlinear Galerkin method: A multiscale method applied to the simulation of homogeneous turbulent flows ⋮ Approximate inertial manifolds of exponential order for semilinear parabolic equations subjected to additive white noise ⋮ Approximate inertial manifolds for retarded semilinear parabolic equations. ⋮ Arbitrarily accurate approximate inertial manifolds of fixed dimension. ⋮ A continuity property for the inverse of Mañé's projection ⋮ Long time behavior for a dissipative shallow water model ⋮ Chaos synchronization for continuous chaotic systems by inertial manifold approach ⋮ Incremental unknowns, multilevel methods and the numerical simulation of turbulence ⋮ Inertial manifolds for nonautonomous infinite dimensional dynamical systems ⋮ Convergent families of approximate inertial manifolds for nonautonomous evolution equations ⋮ Convergence of a chaotic attractor with increased spatial resolution of the Ginzburg-Landau equation. ⋮ A sufficient condition for the existence of approximate inertial manifolds containing the global attractor.

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