A Remark on Quasi-Stationary Approximate Inertial Manifolds for the Navier–Stokes Equations

DOI10.1137/S0036141092230428zbMath0808.35102MaRDI QIDQ4302326

Don A. Jones, Edriss S. Titi

Publication date: 14 August 1994

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

zbMATH Keywords

nonlinear Galerkin methodsapproximate inertial manifolds

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Navier-Stokes equations (35Q30) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99) Numerical methods for partial differential equations, boundary value problems (65N99)

Related Items (22)

Approximation of exponential order of the attractor of a turbulent flow ⋮ Regularity and asymptotic behavior of solutions of nonautonomous differential equations ⋮ On the effectiveness of the approximate inertial manifold -- a computational study ⋮ On computing the long-time solution of the two-dimensional Navier-Stokes equations ⋮ Approximate inertial manifolds of exponential order for semilinear parabolic equations subjected to additive white noise ⋮ On the Rate of Convergence of the Nonlinear Galerkin Methods ⋮ Variational representation of the projection dynamics and random motion of highly dissipative systems ⋮ Nonlinear feedback control of parabolic partial differential equation systems with time-dependent spatial domains ⋮ On some dissipative fully discrete nonlinear Galerkin schemes for the Kuramoto-Sivashinsky equation ⋮ A continuity property for the inverse of Mañé's projection ⋮ Gevrey regularity for Navier-Stokes equations under Lions boundary conditions ⋮ A pseudospectral quadrature method for Navier-Stokes equations on rotating spheres ⋮ Reduced-order-based feedback control of the Kuramoto--Sivashinsky equation ⋮ Bifurcation computations on an approximate inertial manifold for the 2D Navier-Stokes equations ⋮ On the persistence of spatial analyticity for the beam equation ⋮ Qualitative features of high lift hovering dynamics and inertial manifolds ⋮ Variational approach to closure of nonlinear dynamical systems: autonomous case ⋮ Nonlinear control of incompressible fluid flow: Application to Burgers' equation and 2D channel flow ⋮ Postprocessing Fourier spectral methods: The case of smooth solutions ⋮ Convergence of a chaotic attractor with increased spatial resolution of the Ginzburg-Landau equation. ⋮ A modified nonlinear spectral Galerkin method for the equations of motion arising in the Kelvin–Voigt fluids ⋮ Computational efficiency and approximate inertial manifolds for a Bénard convection system

This page was built for publication: A Remark on Quasi-Stationary Approximate Inertial Manifolds for the Navier–Stokes Equations