Exponential attractor for a planar shear-thinning flow

✍ Scribed by Dalibor Pražák

• Publisher: John Wiley and Sons
• Year: 2007
• Tongue: English
• Weight: 168 KB
• Volume: 30
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.885

✦ Synopsis

Abstract

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 𝓁‐trajectories. Copyright © 2007 John Wiley & Sons, Ltd.