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On non-Newtonian incompressible fluids with phase transitions

✍ Scribed by Namkwon Kim; Luisa Consiglieri; José Francisco Rodrigues

Publisher
John Wiley and Sons
Year
2006
Tongue
English
Weight
182 KB
Volume
29
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

A modified model for a binary fluid is analysed mathematically. The governing equations of the motion consists of a Cahn–Hilliard equation coupled with a system describing a class of non‐Newtonian incompressible fluid with p‐structure. The existence of weak solutions for the evolution problems is shown for the space dimension d=2 with p⩾ 2 and for d=3 with p⩾ 11/5. The existence of measure‐valued solutions is obtained for d=3 in the case 2⩽ p< 11/5. Similar existence results are obtained for the case of nondifferentiable free energy, corresponding to the density constraint |ψ| ⩽ 1. We also give regularity and uniqueness results for the solutions and characterize stable stationary solutions. Copyright © 2006 John Wiley & Sons, Ltd.

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