Inertial manifolds for the Kuramoto-Sivashinsky equation and an estimate of their lowest dimension
From MaRDI portal
Publication:909097
zbMath0694.35028MaRDI QIDQ909097
Basil Nicolaenko, George R. Sell, Roger M. Temam, Ciprian Foias
Publication date: 1988
Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)
dimensionKuramoto-Sivashinsky equationinertial Lipschitz manifoldinvariant cone propertystrong squeezing property
Initial-boundary value problems for higher-order parabolic equations (35K35) Periodic solutions to PDEs (35B10) Linear higher-order PDEs (35G05)
Related Items
Hyperdissipative Navier–Stokes Equations Driven by Time-Dependent Forces: Invariant Manifolds, \(H^1\) solutions for a Kuramoto-Sinelshchikov-Cahn-Hilliard type equation, The invariant manifold approach applied to global long-time dynamics of FitzHugh-Nagumo systems, On the dynamics of aeolian sand ripples, Inertial manifolds for 3D complex Ginzburg-Landau equations with periodic boundary conditions, Stability enhancement by boundary control in the Kuramoto-Sivashinsky equation, Perturbations of normally hyperbolic manifolds with applications to the Navier-Stokes equations, On the stochastic Kuramoto-Sivashinsky equation, On the non-homogeneous stationary Kuramoto-Sivashinsky equation, Inertial manifolds for Burgers' original model system of turbulence, The Kuramoto-Sivashinsky equation: a bridge between PDE's and dynamical systems, Collections of heteroclinic cycles in the Kuramoto-Sivashinsky equation, Full discrete nonlinear Galerkin method for the Navier-Stokes equations, Optimal bounds on the Kuramoto-Sivashinsky equation, Global error analysis and inertial manifold reduction, Order and complexity in the Kuramoto-Sivashinsky model of weakly turbulent interfaces, Inertial manifolds for nonlinear evolutionary equations, A flexible symmetry-preserving Galerkin/POD reduced order model applied to a convective instability problem, Trivial stationary solutions to the Kuramoto-Sivashinsky and certain nonlinear elliptic equations, Some closure results for inertial manifolds, Fractional Kuramoto-Sivashinsky equation with power law and stretched Mittag-Leffler kernel, On the initial-boundary value problem for a Kuramoto-Sinelshchikov type equation, Stability Analysis of the Nonlinear Galerkin Method, Forced symmetry breaking of homoclinic cycles in a PDE with O(2) symmetry, Inertial manifolds for the hyperviscous Navier-Stokes equations, Dynamics of a nonlocal Kuramoto-Sivashinsky equation, Finite-dimensional asymptotic behavior for the Swift-Hohenberg model of convection, The viscous Cahn-Hilliard equation with inertial term, Zero dynamics boundary control for regulation of the Kuramoto-Sivashinsky equation, Initial value problem and asymptotic low dimensional behavior in the Kuramoto-Velarde equation, Global solutions in higher dimensions to a fourth-order parabolic equation modeling epitaxial thin-film growth, Local exact controllability to the trajectories of the 1-D Kuramoto-Sivashinsky equation, \(H^1\) solutions for a Kuramoto-Velarde type equation, The singular limit dynamics of the phase-field equations, A POD/Galerkin model from eigenfunctions of non-converged Newton iterations in a convection problem, An adaptive high-order minimum action method, On the Rate of Convergence of the Nonlinear Galerkin Methods, A linearized Kuramoto-Sivashinsky PDE via an imaginary-Brownian-time-Brownian-angle process, Local attractors in a certain boundary-value problem for the Kuramoto-Sivashinsky equation, Induced trajectories and approximate inertial manifolds for the Ginzburg- Landau partial differential equation, Estimating the number of asymptotic degrees of freedom for nonlinear dissipative systems, On a diffusion model for growth and dispersal in a population, Spectral barriers and inertial manifolds for dissipative partial differential equations, Nonlinear Galerkin methods: The finite elements case, Approximate inertial manifolds for the Kuramoto-Sivashinsky equation: Analysis and computations, On the use of POD-based ROMs to analyze bifurcations in some dissipative systems, Inertial manifolds for the Kuramoto-Sivashinsky equation, On some dissipative fully discrete nonlinear Galerkin schemes for the Kuramoto-Sivashinsky equation, A concise proof of the geometric construction of inertial manifolds, Attractors and finite-dimensional behaviour in the 2D Navier-Stokes equations, Preserving dissipation in approximate inertial forms for the Kuramoto- Sivashinsky equation, Optimal parameter-dependent bounds for Kuramoto-Sivashinsky-type equations, Gevrey class regularity and approximate inertial manifolds for the Kuramoto-Sivashinsky equation, Smooth invariant foliations in infinite dimensional spaces, Localization and approximation of attractors for the Ginzburg-Landau equation, A continuity property for the inverse of Mañé's projection, Existence and continuity of inertial manifolds for the hyperbolic relaxation of the viscous Cahn-Hilliard equation, Steady state bifurcations for the Kuramoto-Sivashinsky equation: a computer assisted proof, L-Kuramoto-Sivashinsky SPDEs in one-to-three dimensions: L-KS kernel, sharp Hölder regularity, and Swift-Hohenberg law equivalence, Inertial manifolds: The non-self-adjoint case, Inertial manifolds for the 3D modified-Leray-\(\alpha \) model with periodic boundary conditions, On approximate inertial manifolds for two and three dimensional turbulent flows, Global solution to the compressible isothermal multipolar fluid, Inertial manifolds for a singularly non-autonomous semi-linear parabolic equations, Convergence of the Kuramoto-Sinelshchikov equation to the Burgers one, Global analysis of the phase portrait for the Kuramoto-Sivashinsky equation, Boundary local null-controllability of the Kuramoto-Sivashinsky equation, Smoothness of inertial manifolds, Some global dynamical properties of a class of pattern formation equations, Reduced-order-based feedback control of the Kuramoto--Sivashinsky equation, A brief biography of George R. Sell, A new global Carleman estimate for the one-dimensional Kuramoto-Sivashinsky equation and applications to exact controllability to the trajectories and an inverse problem, Spectral barriers and inertial manifolds for time- discretized dissipative equations, Inertial manifolds associated to partly dissipative reaction-diffusion systems, Explicit construction of an inertial manifold for a reaction diffusion equation, Well-posedness of the classical solution for the Kuramto-Sivashinsky equation with anisotropy effects, Exponential tracking and approximation of inertial manifolds for dissipative nonlinear equations, LYAPUNOV EXPONENTS OF THE KURAMOTO–SIVASHINSKY PDE, Inertial manifolds for the 3D modified-Leray-\( \alpha\) model, Inertial manifolds for a Smoluchowski equation on the unit sphere, The Kuramoto-Sivashinsky equation revisited: low-dimensional corresponding systems, Analyticity for Kuramoto-Sivashinsky-type equations in two spatial dimensions, Do inertial manifolds apply to turbulence?, The Bang-bang principle of time optimal controls for the Kuramoto-Sivashinsky-KdV equation with internal control, Existence of inertial manifolds for partly dissipative reaction diffusion systems in higher space dimensions, Persistence of invariant sets for dissipative evolution equations, Inertial manifolds and normal hyperbolicity, On the influence of the geometric characteristics of the region on nanorelief structure, On approximate inertial manifolds to the Navier-Stokes equations, Comparison of sequential data assimilation methods for the Kuramoto-Sivashinsky equation, Well-posedness result for the Kuramoto-Velarde equation, Approximation theories for inertial manifolds, Induced trajectories and approximate inertial manifolds, A geometric method for infinite-dimensional chaos: symbolic dynamics for the Kuramoto-Sivashinsky PDE on the line, \textit{A priori} analysis of reduced description of dynamical systems using approximate inertial manifolds, Variational approach to closure of nonlinear dynamical systems: autonomous case, On the solutions for a Benney-Lin type equation, A unified approach to compute foliations, inertial manifolds, and tracking solutions, CONVERGENCE OF THE SOLUTIONS ON THE GENERALIZED KORTEWEG–DE VRIES EQUATION∗, A note on the computation of bifurcation diagrams of the Kuramoto- Sivashinsky equation by pseudospectral methods, Stackelberg-Nash exact controllability for the Kuramoto-Sivashinsky equation with boundary and distributed controls, Inertial Manifolds via Spatial Averaging Revisited, Inertial Manifolds for Certain Subgrid-Scale $\alpha$-Models of Turbulence, Numerical Computations and Computer Assisted Proofs of Periodic Orbits of the Kuramoto--Sivashinsky Equation, Stabilized neural ordinary differential equations for long-time forecasting of dynamical systems, Dissipativity, analyticity and viscous shocks in the (de)stabilized Kuramoto-Sivashinsky equation, Construction of Bifurcation Diagrams Using POD on the Fly, Computational efficiency and approximate inertial manifolds for a Bénard convection system, Fredholm transform and local rapid stabilization for a Kuramoto-Sivashinsky equation
