Fractal dimension, attractors, and the Boussinesq approximation in three dimensions

DOI10.1007/BF00995132zbMath0815.35084MaRDI QIDQ1341889

Josef Málek, Gudrun Thäter, Michael Ružička

Publication date: 27 June 1995

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

zbMATH Keywords

attractorfractal dimensionBérnard problem

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Navier-Stokes equations (35Q30) Fractals (28A80)

Related Items (10)

On an iterative method for approximate solutions of a generalized Boussinesq model ⋮ Weak-strong uniqueness for heat conducting non-Newtonian incompressible fluids ⋮ Smoothing and finite-dimensionality of uniform attractors in Banach spaces ⋮ Hausdorff and fractal dimensions of attractors for functional differential equations in Banach spaces ⋮ Local well-posedness for Boussinesq approximation with shear dependent viscosities in 3D ⋮ Buoyancy-driven viscous flow with \(L^1\)-data ⋮ The Periodic Initial Value Problem and Initial Value Problem for the Non-Newtonian Boussinesq Approximation ⋮ Finite-dimensionality of tempered random uniform attractors ⋮ Finite-dimensional negatively invariant subsets of Banach spaces ⋮ An existence theorem for the Boussinesq equations with non-Dirichlet boundary conditions.

Cites Work

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• Infinite-dimensional dynamical systems in mechanics and physics
• Global lyapunov exponents, kaplan-yorke formulas and the dimension of the attractors for 2D navier-stokes equations
• Attractors for the Bénard problem: existence and physical bounds on their fractal dimension
• Characteristics-based methods applied to infinite Prandtl number thermal convection in the hard turbulent regime
• Young Measure‐Valued Solutions for Non-Newtonian Incompressible Fluids¹
• ON THE NON-NEWTONIAN INCOMPRESSIBLE FLUIDS

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