An analytical solution method for the unsteady, unbounded, incompressible three-dimensional Navier-Stokes equations in Cartesian coordinates using coordinate axis symmetry degeneracy

Abstract

Analytical solutions are developed for the unsteady Navier-Stokes equations for incompressible fluids in unbounded flow systems with external, time-dependent driving pressure gradients using the degeneracy of the (1 1 1) axis to reduce the inherent non-linearity of the coupled partial differential equations, which is normally performed with boundary conditions. These solutions are then extended to all directions through rotation of the reference axis, yielding a general solution set. While the solutions are self-consistent and developed from a physical understanding of flow systems, they have not been proven unique or applied to experimental data.

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