Preamble

The nature of viscoelasticity, difficulties in proving the existence and uniqueness of the solution of the set of field equations defining a given viscoelastic fluid flow problem, which form the basis of numerical solutions, the high Weissenberg problem, limiting value of the Weissenberg number in computations, the role of singularities and mesh size in computational Rheology, Hadamard instability, and well-posed Cauchy problems are discussed in setting up the stage for constitutive formulations for non-linear viscoelastic fluids. © 2014, The Author(s).