Abstract
Possible statements of eigenvalue problems generalizing the classical Orr-Sommerfeld problem are given for incompressible stationary flows of non-Newtonian fluids; these problems are interpreted within the mechanics of a continuum as problems of the shear stability of such flows. A schematic diagram of the integral relation method as applied to these flows is described. In the case of an unperturbed Couette flow, Joseph estimates are generalized for any type of rheological curve and domains of guaranteed stability are constructed on a plane with the axes showing Reynolds numbers corresponding to the tangent and secant dynamic viscosity at one point.
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