A New Formulation of the Three-dimensional Velocity-Vorticity System in Viscous Incompressible Flow

Abstract

The aim of this work is to study a formulation of the system of equations that governs incompressible viscous flows, in terms of the velocity and the vorticity fields. Such formulation incorporates a set of boundary conditions particularly suitable for the uncoupled solution of this system. The issues concerning the existence and uniqueness of solutions are addressed, and the equivalence with the standard primitive variable formulation is demonstrated, in a rigorous mathematical context.