Arbitrary Motions of a Viscous Incompressible Liquid in a Finite Region

Abstract

By using an entirely constructive analysis it is shown that there exist solutions of the viscous flow equations in which two of the Cartesian components of velocity are arbitrary and the third component can be constructed uniquely by the application of integrability conditions. The solutions are in general defined in a finite region of the fluid and can be matched onto a well‐defined deterministic solution of the Navier–Stokes equations such that all of the relevant physical quantities are continuous at the interface.