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 equatio ns (PDEs) in Fluid Mechanics. In this context, boundary- or initial co nditions are disregarded. The PDEs under consideration are the classic al Navier-Stokes equations and two versions of tile Nehring equations. The families of solutions depend on coefficients in the PDEs and on f ree coefficients as generated in the construction. Regarding the struc tures of the solutions of systems of PDEs, possibilities of their comp arisons by means of these families are discussed For the systems of PD Es under consideration, in particular, families are constructed that a re represented by traveling waves. Employing the essentially explicit representations of families of solutions, conclusions are drawn concer ning, e.g., (a) the occurrence of bounded or unbounded solutions, (b) the dependency of the wave speed on transport coefficients, and (c) th e limiting case of the vanishing of a transport coefficient.