Exponential attractors and their relevance to fluid dynamics systems

DOI10.1016/0167-2789(93)90116-IzbMath0790.34053MaRDI QIDQ1803769

Zhen-Su She, Alp Eden, Ciprian Foias, Basil Nicolaenko

Publication date: 29 June 1993

Published in: Physica D (Search for Journal in Brave)

zbMATH Keywords

Kuramoto-Sivashinsky equation2D Navier-Stokes equationsexponential attractorsinfinite dimensional dynamical systemsenstrophy spaceparabolic P.D.E.

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Navier-Stokes equations for incompressible viscous fluids (76D05) Nonlinear differential equations in abstract spaces (34G20) Navier-Stokes equations (35Q30) Attractors of solutions to ordinary differential equations (34D45) Dynamical systems and ergodic theory (37-XX)

Related Items (7)

Exponential attractors of optimal Lyapunov dimension for Navier-Stokes equations ⋮ Exponential attractors of reaction-diffusion systems in an unbounded domain ⋮ Parametrising the attractor of the two-dimensional Navier-Stokes equations with a finite number of nodal values ⋮ A continuity property for the inverse of Mañé's projection ⋮ Parametrising the attractor of the two-dimensional Navier-Stokes equations with a finite number of nodal values ⋮ Statistical decomposition of chaotic attractors by the eigenvectors of Oseledec matrix -- Active and passive information dynamics ⋮ Local attractors for weakly damped forced KdV equation in thin 2D domains

Cites Work

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• Some global dynamical properties of the Kuramoto-Sivashinsky equations: nonlinear stability and attractors
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• On the dimension of the attractors in two-dimensional turbulence
• Integral manifolds and inertial manifolds for dissipative partial differential equations
• Infinite-dimensional dynamical systems in mechanics and physics.
• Approximate inertial manifolds and effective viscosity in turbulent flows
• Diffusion Approximation for Turbulent Scalar Fields

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