Systematic linearization for stability of shear flows of viscoelastic fluids (Q1082181)

Based on the latest studies by \textit{U. Akbay}, \textit{E. Becker}, \textit{S. Krozer} and \textit{S. Sponagel} [Mech. Res. Commun. 7, 199-204 (1980; Zbl 0439.76002)] and \textit{U. Akbay} and \textit{S. Sponagel} [Rheol. Acta. 20, 579-590 (1981; Zbl 0477.76003)], authors have solved the titled problem for the history of a simple fading memory. It has been shown that periodic disturbances of long wave length in the flow direction may lead to instability when modified Weissenberg number function \[ \eta \cdot (d(\eta \chi)/d\chi)^{-1}\cdot \quad [\chi /\eta \cdot \quad d/d\chi (N_ 1/\chi)]^ 2 \] (\(\kappa\)-shear rate, \(\eta\) (\(\kappa)\)-shear viscosity function, \(N_ 1(\chi)\)-first normal stress difference) is sufficiently large and the memory of the fluid is short.