Comparison of classical and alternative fluid equations using symmetry methods

Employing symmetry groups and -reductions, families of exact solutions are constructed for systems of nonlinear partial differential equations (PDEs) in Fluid Mechanics. In this context, boundary- or initial conditions are disregarded. The PDEs under consideration are the classical Navier-Stokes equations and two versions of the Nehring equations. The families of solutions depend on coefficients in the PDEs and on free coefficients as generated in the construction. Regarding the structures of the solutions of systems of PDEs, possibilities of their comparisons by means of these families are discussed For the systems of PDEs under consideration, in particular, families are constructed that are represented by traveling waves. Employing the essentially explicit representations of families of solutions, conclusions are drawn concerning, e.g., (a) the occurrence of bounded or unbounded solutions, (b) the dependency of the wave speed on transport coefficients, and (c) the limiting case of the vanishing of a transport coefficient.