Fractal dimension,attractors, and the boussinesq approximation in three dimensions |
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Authors: | Josef Málek Michael RůŽička Gudrun ThÄter |
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Institution: | (1) Institute of Applied Mathematics, Beringstrae 4-6, D-53115 Bonn, Germany;(2) Fachbereich 17, University of Paderbom, Warburger Strae 100, D-33098 Paderborn, Germany |
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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. |
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Keywords: | 35B40 35Q72 35K55 |
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