On some unresolved issues in non-linear fluid dynamics

This paper is a discussion of some open problems concerning generalizations of Navier–Stokes fluids and other non-linear fluids, which are in need of thorough investigation. The first topic is an interesting generalization of the Navier–Stokes model which is appropriate, in particular, in the description of fluids like water subjected to processes in which the normal stresses are very large. Discussed next is the modelling of non-Newton fluids at a distance from the boundary of the volume occupied by the fluid. Attention is then given to the necessity of a careful revision of conditions obtained at the boundary of the fluid volume, and finally, the modelling of “turbulent” flows is discussed.