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Acta Applicandae Mathematica

, Volume 37, Issue 1–2, pp 83–97 | Cite as

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

  • Josef Málek
  • Michael RůŽička
  • Gudrun ThÄter
Article

Abstract

The Boussinesq approximation, where the viscosity depends polynomially on the shear rate, finds more and more frequent use in geological practice. In the paper, this modified Boussinesq approximation is investigated as a dynamical system for which the existence of a global attractor is proved. Finally, a new criterion for estimating the fractal dimension of invariant sets is formulated and its application to the problem under consideration is illustrated.

Mathematics subject classification (1991)

35B40 35Q72 35K55 

Key words

fractal dimension attractor Bernard problem 

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Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • Josef Málek
    • 1
  • Michael RůŽička
    • 1
  • Gudrun ThÄter
    • 2
  1. 1.Institute of Applied MathematicsBonnGermany
  2. 2.Fachbereich 17University of PaderbomPaderbornGermany

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