Large time behavior via the method of $\ell$-trajectories

DOI10.1006/jdeq.2001.4087zbMath1187.37113OpenAlexW2092297307MaRDI QIDQ1614726

Publication date: 8 September 2002

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jdeq.2001.4087

zbMATH Keywords

global attractor large time behavior exponential attractor finite fractal dimension power-law fluids $\ell$-trajectory fluids with shear-dependent viscosity

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Attractors (35B41) PDEs in connection with fluid mechanics (35Q35) Navier-Stokes equations for incompressible viscous fluids (76D05) Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems (37L30) Nonlinear differential equations in abstract spaces (34G20)

Related Items

Semilinear damped wave equation in locally uniform spaces ⋮ Existence of a global attractor for the parabolic equation with nonlinear Laplacian principal part in an unbounded domain ⋮ Dynamics for generalized incompressible Navier-Stokes equations in $\mathbb{R}^2$ ⋮ A note on the dimension of the global attractor for an abstract semilinear hyperbolic problem ⋮ Finite dimensional smooth attractor for the Berger plate with dissipation acting on a portion of the boundary ⋮ Differentiability of the solution operator and the dimension of the attractor for certain power--law fluids ⋮ Quantum Zakharov model in a bounded domain ⋮ Quasi-stability and exponential attractors for a non-gradient system -- applications to piston-theoretic plates with internal damping ⋮ GLOBAL AND EXPONENTIAL ATTRACTORS FOR THE PENROSE–FIFE SYSTEM ⋮ Reaction-diffusion systems with supercritical nonlinearities revisited ⋮ Continuous data assimilation for the 3D Ladyzhenskaya model: analysis and computations ⋮ Long term dynamics of second order-in-time stochastic evolution equations with state-dependent delay ⋮ A variational approach to a Cahn-Hilliard model in a domain with nonpermeable walls ⋮ Longtime dynamics of the quasi-linear wave equations with structural damping and supercritical nonlinearities ⋮ Finite-dimensional attractors for the Kirchhoff equation with a strong dissipation ⋮ Nonlinear dynamical analysis for globally modified incompressible non-Newtonian fluids ⋮ The global existence and attractor for $p$-Laplace equations in unbounded domains ⋮ Exponential attractors for semigroups in Banach spaces ⋮ Pullback attractors with finite fractal dimension for a semilinear transfer equation with delay in some non-cylindrical domain ⋮ Finite fractal dimensional pullback attractors for a class of 2D magneto-viscoelastic flows ⋮ Existence of exponential attractor to p(x)‐Laplacian via the l‐trajectories method ⋮ Attractors. Then and now ⋮ A necessary and sufficient condition for the existence of an exponential attractor ⋮ THE EXISTENCE OF PULLBACK EXPONENTIAL ATTRACTORS FOR NONAUTONOMOUS DYNAMICAL SYSTEM AND APPLICATIONS TO NONAUTONOMOUS REACTION DIFFUSION EQUATIONS ⋮ Necessary and sufficient conditions for the existence of exponential attractors for semigroups, and applications ⋮ Long-time dynamics of Kirchhoff wave models with strong nonlinear damping ⋮ On global in time dynamics of a planar Bingham flow subject to a subdifferential boundary condition ⋮ Asymptotic behavior for the quasi-geostrophic equations with fractional dissipation in $\mathbb{R}^2$ ⋮ Long-time dynamics for a class of Kirchhoff models with memory ⋮ Dynamics of second order in time evolution equations with state-dependent delay ⋮ Convergence to steady state and attractors for doubly nonlinear equations ⋮ Global exponential $\kappa$-dissipative semigroups and exponential attraction ⋮ On an anisotropic doubly nonlinear Allen-Cahn equation with singular potentials ⋮ Dynamics of weak solutions for the three dimensional Navier-Stokes equations with nonlinear damping ⋮ Global attractors for small samples and germs of 3D Navier-Stokes equations ⋮ Attractors for 2D-Navier-Stokes models with delays ⋮ Attractors for nonlinear reaction-diffusion systems in unbounded domains via the method of short trajectories ⋮ Long-term analysis of degenerate parabolic equations in $\mathbb R^N$ ⋮ Finite Dimensionality of the Attractor for a Semilinear Wave Equation with Nonlinear Boundary Dissipation ⋮ Exponential attractors for abstract parabolic systems with bounded delay ⋮ Finite dimensional global attractor for a class of doubly nonlinear parabolic equations ⋮ Pullback exponential attractors for the three dimensional non-autonomous Navier-Stokes equations with nonlinear damping ⋮ RECENT DEVELOPMENTS IN DYNAMICAL SYSTEMS: THREE PERSPECTIVES ⋮ COMPARISON BETWEEN TRAJECTORY AND GLOBAL ATTRACTORS FOR EVOLUTION SYSTEMS WITHOUT UNIQUENESS OF SOLUTIONS ⋮ Pullback exponential attractors for a class of non-Newtonian micropolar fluids ⋮ On the 2D Cahn–Hilliard Equation with Inertial Term ⋮ On the dimension of global attractor for the Cahn-Hilliard-Brinkman system with dynamic boundary conditions ⋮ Attractors and long-time behavior of von Kármán thermoelastic plates ⋮ Analysis of the Cahn–Hilliard Equation with a Chemical Potential Dependent Mobility ⋮ Existence and upper semicontinuity of attractors for a class of non-Newtonian micropolar fluids ⋮ Exponential attractors for reaction-diffusion equations with arbitrary polynomial growth ⋮ Global attractor for a wave equation with nonlinear localized boundary damping and a source term of critical exponent ⋮ Finite-dimensional attractors for the quasi-linear strongly-damped wave equation ⋮ Pullback exponential attractors for the viscous Cahn-Hilliard-Navier-Stokes system with dynamic boundary conditions ⋮ Finite-dimensional attractors for the Kirchhoff models ⋮ Pullback Exponential Attractors for Nonautonomous Reaction–Diffusion Equations ⋮ Attractors for the inhomogeneous incompressible Navier-Stokes flows ⋮ Attractors for stochastic reaction-diffusion equation with additive homogeneous noise ⋮ Finite-dimensional attractors for the Kirchhoff models with critical exponents ⋮ On Fractal Dimension of Global and Exponential Attractors for Dissipative Higher Order Parabolic Problems in $$\mathbb {R}^N$$ with General Potential ⋮ ATTRACTORS FOR A CAGINALP MODEL WITH A LOGARITHMIC POTENTIAL AND COUPLED DYNAMIC BOUNDARY CONDITIONS ⋮ Dynamics of the three-dimensional primitive equations of large-scale atmosphere ⋮ A survey on Navier-Stokes models with delays: existence, uniqueness and asymptotic behavior of solutions

Cites Work

This page was built for publication: Large time behavior via the method of $\ell$-trajectories

Large time behavior via the method of \(\ell\)-trajectories