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Fractal dimension, attractors, and the boussinesq approximation in three dimensions (1994)

Málek, Josef ; RůŽička, Michael ; ThÄter, Gudrun

Springer

Acta applicandae mathematicae 37 (1994), S. 83-97

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ISSN: 1572-9036

Keywords: 35B40 ; 35Q72 ; 35K55 ; fractal dimension ; attractor ; Bernard problem

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: 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.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF00995132

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