Abstract
AbstractA 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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