Nonlinear viscoelasticity theoretical results

From a fundamental point of view, none of the theoretical results necessary to justify rigorously bifurcation or stability studies have been fully established so far for the equations governing viscoelastic flows (contrary to the Newtonian case). Such results concern, for instance, the relations between linear stability and the spectrum of the associated operator, between linear and nonlinear stability, or the reduction of the dynamics to a centre manifold. 

The described universal scenario of shear-molten glass and shear-thinnig fluid makes up the core of the MCT-ITT predictions derived from (11-14). Their consequences for the nonlinear rheology will be discussed in more detail in the following sections, while the MCT results for the linear viscoelasticity were reviewed in Sect. 3. Yet, the anisotropy of the equations has up to now prevented more complete solutions of the MCT-ITT equations of Sect. 2. Therefore, simplified MCT-ITT equations become important, which can be analysed in more detail and recover the central stability equations (20, 22). The two most important ones will be reviewed next, before the theoretical picture is tested in comparison with experimental and simulations data. 

---