Some properties and analytical expressions forplane flow of Leonov and Giesekus models

In a recent paper by Van der Zanden and Hulsen [1], some properties andanalytical expressions for the plane flow of the Leonov and Giesekus modelsare used without proof. This paper is concerned with the derivation of theseproperties and expressions, involving restrictions on the extra-stress tensors, which are important for the well-posedness of the system of equations,analytical expressions for steady linear flows,the possibility of non-linear instabilities due to numerical approximationerrors.After defining the Leonov and Giesekus models the problems given abovewill be treated in separate sections.