Finite-dimensionality of bounded invariant sets for Navier-Stokes systems and other dissipative systems

DOI10.1007/BF02112336zbMath0561.76044MaRDI QIDQ2266640

O. A. Ladyzhenskaya

Publication date: 1985

Published in: Journal of Soviet Mathematics (Search for Journal in Brave)

zbMATH Keywords

attractorfunctional invariant setsfinite Hausdorff dimension

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Nonlinear effects in hydrodynamic stability (76E30) Navier-Stokes equations (35Q30)

Related Items (23)

On dimension and metric properties of trajectory attractors ⋮ Asymptotic behaviour of solutions to nonlinear shells in a supersonic flow¹ ⋮ Limit behavior and on the attractor for the equations of motion of Oldroyd fluids ⋮ Attractors of nonlinear evolution problems with dissipation ⋮ Attractors and dynamical systems generated by initial-boundary problems for the equations of motion of viscoelastic fluids ⋮ Accelerating waveform relaxation methods with application to parallel semiconductor device simulation^∗ ⋮ Parameterizing the global attractor of the navier-stokes equations by nodal values ⋮ Attractors. Then and now ⋮ Pullback exponential attractors with explicit fractal dimensions for non-autonomous partial functional differential equations ⋮ Attractors for Nonautonomous Navier–Stokes System and Other Partial Differential Equations ⋮ Properties of the attractor in the problem of the nonlinear vibrations of an infinite panel ⋮ Global behavior of the solutions of certain fourth-order nonlinear equations ⋮ Estimates for the fractal dimension and the number of determining modes for invariant sets of dynamical systems ⋮ Global attractors for von Karman evolutions with a nonlinear boundary dissipation. ⋮ On the finite dimensionality of random attractors¹ ⋮ Finite dimensionality and regularity of attractors for a 2-D semilinear wave equation with nonlinear dissipation ⋮ Finite Dimensionality of the Attractor for a Semilinear Wave Equation with Nonlinear Boundary Dissipation ⋮ Dynamical system generated by the equations of motion of an Oldroyd fluid of order L ⋮ Dynamical system generated by the equations of motion of an Oldroyd fluid of order L ⋮ Measure-valued solutions and asymptotic behavior of a multipolar model of a boundary layer ⋮ Existence of inertial manifolds for partly dissipative reaction diffusion systems in higher space dimensions ⋮ Hausdorff dimension of a random invariant set ⋮ Pullback dynamics of 3D Navier-Stokes equations with nonlinear viscosity

Cites Work

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• Hopf's conjecture for a class of chemical kinetics equations
• Limit states for modified Navier-Stokes equations in three-dimensional space
• Some analytic and geometric properties of the solutions of the evolution Navier-Stokes equations
• A dynamical system generated by the Navier-Stokes equations
• Negatively invariant sets of compact maps and an extension of a theorem of Cartwright
• HYPERBOLIC LIMIT SETS OF EVOLUTIONARY EQUATIONS AND THE GALERKIN METHOD
• Almost Periodic Flows and Solutions of Differential Equations
• A mathematical example displaying features of turbulence

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