In this chapter we present the form of the Navier–Stokes equations implied by the Helmholtz decomposition in which the relation of the irrotational and rotational velocity fields is made explicit. The idea of self-equilibration of irrotational viscous stresses is introduced. The decomposition is constructed first by selection of the irrotational flow compatible with the flow boundaries and other prescribed conditions. The rotational component of velocity is then the difference between the solution of the Navier–Stokes equations and the selected irrotational flow. To satisfy the boundary conditions, the irrotational field is required, and it depends on the viscosity. Five unknown fields are determined by the decomposed form of the Navier–Stokes equations for an incompressible fluid: the three rotational components of velocity, the pressure, and the harmonic potential. These five fields may be readily identified in analytic solutions available in the literature. It is clear from these exact solutions that potential flow of a viscous fluid is required for satisfying prescribed conditions, such as the no-slip condition at the boundary of a solid or continuity conditions across a two-fluid boundary. The decomposed form of the Navier–Stokes equations may be suitable for boundary layers because the target irrotational flow that is expected to appear in the limit, say at large Reynolds numbers, is an explicit to-be-determined field.