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Exponential attractor for a planar shear‐thinning flow
Author(s) -
Pražák Dalibor
Publication year - 2007
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.885
Subject(s) - mathematics , attractor , exponential function , mathematical analysis , shear thinning , cauchy stress tensor , compressibility , fractal dimension , power law , fractal , physics , viscosity , mechanics , statistics , quantum mechanics
We study the dynamics of an incompressible, homogeneous fluid of a power‐law type, with the stress tensor T = ν(1 + µ| Dv |) p −2 Dv , where Dv is a symmetric velocity gradient. We consider the two‐dimensional problem with periodic boundary conditions and p ∈ (1, 2). Under these assumptions, we estimate the fractal dimension of the exponential attractor, using the so‐called method of ‐trajectories. Copyright © 2007 John Wiley & Sons, Ltd.