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Unconditional non‐linear stability for a fluid of third grade
Author(s) -
Budu Paula
Publication year - 2004
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.466
Subject(s) - mathematics , stability (learning theory) , viscosity , linear stability , fluid dynamics , function (biology) , thermodynamics , mathematical analysis , mechanics , physics , instability , computer science , machine learning , evolutionary biology , biology
The thermal convection in a layer of a third grade fluid is investigated, with viscosity being a general function of temperature. We develop a non‐linear stability analysis and prove that unconditional non‐linear stability criterion is achieved using a natural energy approach. This shows that, in some sense, the equations for a fluid of third grade are preferable to those for a fluid of second grade or a dipolar fluid. Copyright © 2004 John Wiley & Sons, Ltd.