Pullback attractors for non-autonomous 2D-Navier--Stokes equations in some unbounded domains

DOI10.1016/j.crma.2005.12.015zbMath1085.37054OpenAlexW2037277440MaRDI QIDQ817901

José Real, Grzegorz Łukaszewicz, Tomás Caraballo Garrido

Publication date: 20 March 2006

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2005.12.015

zbMATH Keywords

pullback attractorpullback asymptotic compactnessnonautonomous dynamical systemuniform attractorspullback absorbing family of sets

Mathematics Subject Classification ID

Attractors (35B41) Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems (37L30) Dynamical systems in fluid mechanics, oceanography and meteorology (37N10) Navier-Stokes equations (35Q30) Linear constitutive equations for materials with memory (74D05) Topological dynamics of nonautonomous systems (37B55)

Related Items

Random attractors for non-autonomous stochastic Brinkman-Forchheimer equations on unbounded domains ⋮ Random attractors for stochastic 2D-Navier-Stokes equations in some unbounded domains ⋮ Pullback Attractors for a Reaction–Diffusion Equation in a General Nonempty Open Subset of ℝN with Nonautonomous Forcing Term in H−1 ⋮ Robustness of nonautonomous attractors for a family of nonlocal reaction-diffusion equations without uniqueness ⋮ Pullback attractors for a damped semilinear wave equation with delays ⋮ Asymptotic behaviour of the nonautonomous SIR equations with diffusion ⋮ Existence and approximation of attractors for nonlinear coupled lattice wave equations ⋮ On the convergence of the uniform attractor of 2D NS-\(\alpha \) model to the uniform attractor of 2D NS system ⋮ Pullback attractor in \(H^{1}\) for nonautonomous stochastic reaction-diffusion equations on \(\mathbb{R}^n\) ⋮ Robustness of time-dependent attractors in \(H^1\)-norm for nonlocal problems ⋮ Pullback attractors for 2D Navier-Stokes equations with delays and the flattening property ⋮ Pullback attractors for the non-autonomous 2D Navier-Stokes equations for minimally regular forcing ⋮ Long term behavior of random Navier-Stokes equations driven by colored noise ⋮ Asymptotic behaviour of nonlocal \(p\)-Laplacian reaction-diffusion problems ⋮ Necessary and sufficient criteria for existence, regularity, and asymptotic stability of enhanced pullback attractors with applications to 3D primitive equations ⋮ Theoretical results on the existence, regularity and asymptotic stability of enhanced pullback attractors: applications to 3D primitive equations ⋮ Random attractors and invariant measures for stochastic convective Brinkman-Forchheimer equations on 2D and 3D unbounded domains ⋮ Random attractors for non-autonomous stochastic Navier-Stokes-Voigt equations in some unbounded domains ⋮ On the Kneser property for reaction-diffusion equations in some unbounded domains with an \(H^{ - 1}\)-valued non-autonomous forcing term ⋮ Pullback attractors for a semilinear heat equation in a non-cylindrical domain ⋮ Dynamics of the three-dimensional Brinkman-Forchheimer-extended Darcy model in the whole space ⋮ \(\mathbb{H}^1\)-random attractors for 2D stochastic convective Brinkman-Forchheimer equations in unbounded domains ⋮ Asymptotically Autonomous Robustness in Probability of Random Attractors for Stochastic Navier-Stokes Equations on Unbounded Poincaré Domains ⋮ Global attractors for a tropical climate model. ⋮ Stability analysis of stochastic 3D Lagrangian-averaged Navier-Stokes equations with infinite delay ⋮ Attractors for a fluid-structure interaction problem in a time-dependent phase space ⋮ Convergence of global attractors of a 2D non-Newtonian system to the global attractor of the 2D Navier-Stokes system ⋮ Pullback attractors of the Jeffreys-Oldroyd equations ⋮ Existence and upper semicontinuity of random pullback attractors for 2D and 3D non-autonomous stochastic convective Brinkman-Forchheimer equations on whole space. ⋮ Sufficient and necessary criteria for existence of pullback attractors for non-compact random dynamical systems ⋮ Asymptotic behavior of the non-autonomous 3D Navier-Stokes problem with coercive force ⋮ Pullback attractors for the non-autonomous reaction-diffusion equations in RN ⋮ Asymptotic behaviour of a non-autonomous Lorenz-84 system ⋮ Attractors for a double time-delayed 2D-Navier-Stokes model ⋮ Invariant measures for non-autonomous dissipative dynamical systems ⋮ Pullback attractors for 2D Navier-Stokes equations on time-varying domains ⋮ \(H^2\)-boundedness of the pullback attractor for the non-autonomous SIR equations with diffusion ⋮ Existence and upper semicontinuity of \((L^2,L^q)\) pullback attractors for a stochastic \(p\)-Laplacian equation ⋮ Pullback attractors of nonautonomous nonclassical diffusion equations with nonlocal diffusion ⋮ Asymptotic behavior of a class of non-autonomous degenerate parabolic equations ⋮ An exponential growth condition in \(H^{2}\) for the pullback attractor of a non-autonomous reaction-diffusion equation ⋮ On pullback attractors for a class of two-dimensional turbulent shear flows ⋮ Continuity and pullback attractors for a non-autonomous reaction-diffusion equation in \(\mathbb R^N\) ⋮ Invariant Borel probability measures for discrete long-wave-short-wave resonance equations ⋮ \(H^2\)-boundedness of the pullback attractors for non-autonomous 2D Navier-Stokes equations in bounded domains ⋮ Pullback attractor for heat convection problem in a micropolar fluid ⋮ Non-autonomous attractors for singularly perturbed parabolic equations on \(\mathbb R^n\) ⋮ Pullback attractors of non-autonomous reaction-diffusion equations in \(H^1_0\) ⋮ Pullback attractors for non-autonomous reaction-diffusion equations with dynamical boundary conditions ⋮ Dynamics for a non-autonomous degenerate parabolic equation in \(\mathfrak{D}_{0}^{1}(\Omega, \sigma)\) ⋮ Pullback attractors for a non-autonomous incompressible non-Newtonian fluid ⋮ Pullback attractors for a weakly damped wave equation with delays and sup-cubic nonlinearity ⋮ ON PULLBACK ATTRACTORS IN $H^1_0$ FOR NONAUTONOMOUS REACTION–DIFFUSION EQUATIONS ⋮ EXISTENCE OF PULLBACK ATTRACTOR FOR A REACTION–DIFFUSION EQUATION IN SOME UNBOUNDED DOMAINS WITH NON-AUTONOMOUS FORCING TERM IN H^-1 ⋮ Regularity results and exponential growth for pullback attractors of a non-autonomous reaction-diffusion model with dynamical boundary conditions ⋮ Well-Posedness and Asymptotic Behavior of a Nonclassical Nonautonomous Diffusion Equation with Delay ⋮ Attractors for non-autonomous retarded lattice dynamical systems ⋮ Pullback attractors for the non-autonomous FitzHugh-Nagumo system on unbounded domains ⋮ Asymptotic behavior of stochastic g-Navier-Stokes equations on a sequence of expanding domains ⋮ Pullback attractor for non-homogeneous micropolar fluid flows in non-smooth domains ⋮ Pullback attractors for a semilinear heat equation on time-varying domains ⋮ Existence and regularity of pullback attractors for an incompressible non-Newtonian fluid with delays ⋮ On \(H^1\)-pullback attractors for nonautonomous micropolar fluid equations in a bounded domain ⋮ On the relation between two different concepts of pullback attractors for non-autonomous dynamical systems ⋮ Pullback attractors in \(V\) for non-autonomous 2D-Navier-Stokes equations and their tempered behaviour ⋮ Pullback attractors for non-autonomous reaction-diffusion equations on \(\mathbb R^n\) ⋮ Asymptotically autonomous dynamics for non-autonomous stochastic \(g\)-Navier-Stokes equation with additive noise ⋮ Attractors for a Nonautonomous Liénard Equation ⋮ Pullback attractors for weak solution to modified Kelvin-Voigt model ⋮ \(H^{2}\)-boundedness of the pullback attractor for a non-autonomous reaction-diffusion equation ⋮ \(L^p\)-pullback attractors for non-autonomous reaction-diffusion equations with delays ⋮ Minimality Properties of Set-Valued Processes and their Pullback Attractors ⋮ Pullback attractors for p-Laplacian equations with delays ⋮ Pullback attractors for 2D MHD equations with delays ⋮ Dynamics for a stochastic reaction-diffusion equation with additive noise ⋮ Long-time behavior of a non-autonomous parabolic equation with nonlocal diffusion and sublinear terms ⋮ Pullback asymptotic behavior of solutions for a non-autonomous non-Newtonian fluid on two-dimensional unbounded domains ⋮ Some new regularity results of pullback attractors for 2D Navier-Stokes equations with delays

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Asymptotic behaviour of nonautonomous difference inclusions
• Random attractors
• Global attractors for damped semilinear wave equations.
• Attractors for noncompact nonautonomous systems via energy equations.
• Pullback attractors for asymptotically compact non-autonomous dynamical systems
• The global attractor for the 2D Navier-Stokes flow on some unbounded domains
• FINITE DIMENSIONALITY OF ATTRACTORS FOR NON-AUTONOMOUS DYNAMICAL SYSTEMS GIVEN BY PARTIAL DIFFERENTIAL EQUATIONS