Geodesic
Stability and bifurcation in viscous incompressible fluids
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 27, Tome 233 (1996), pp. 9-29 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider heat-conducting viscous incompressible (not necessarily Newtonian) fluids under the general Stokesian constitutive hypotheses. Given a natural and mild condition on the stress tensor at vanishing velocity, that is satisfied for Newtonian fluids, we discuss the stability behavior of stationary states at which the fluid is at rest and at constant temperature. In particular we prove the existence of global small strong solutions for rather general isothermal non-Newtonian fluids. We also study bifurcation problems and show that subcritical bifurcations can occur. This effect can be seen only if the full energy equation is taken into consideration, that is, if the energy dissipation term is not dropped, as is done in the usual Boussinesq approximation. Bibl. 29 titles. 
@article{ZNSL_1996_233_a1,
     author = {H. Amann},
     title = {Stability and bifurcation in viscous incompressible fluids},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {9--29},
     year = {1996},
     volume = {233},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1996_233_a1/}
}
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H. Amann. Stability and bifurcation in viscous incompressible fluids. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 27, Tome 233 (1996), pp. 9-29. http://geodesic.mathdoc.fr/item/ZNSL_1996_233_a1/