On non‐Newtonian incompressible fluids with phase transitions | Zendy

Kim Namkwon | Zendy; Consiglieri Luisa | Zendy; Rodrigues José Francisco | Zendy

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On non‐Newtonian incompressible fluids with phase transitions

Author(s) -

Kim Namkwon,

Consiglieri Luisa,

Rodrigues José Francisco

Publication year - 2006

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.739

Subject(s) - mathematics , uniqueness , compressibility , constraint (computer aided design) , newtonian fluid , dimension (graph theory) , mathematical analysis , weak solution , space (punctuation) , non newtonian fluid , class (philosophy) , motion (physics) , mathematical physics , pure mathematics , classical mechanics , thermodynamics , geometry , physics , linguistics , philosophy , artificial intelligence , computer science

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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