TABLE OF CONTENTS Our aim in this section is to return to, and study in more detail, the equations of motion of a Newtonian fluid as well as the boundary conditions that are associated with them.
Throughout this chapter, the fluid is represented by a material system S that fills the domain ? 0 at time t = 0 and the domain ? t at time t. We may have ? t = ? 0, which corresponds, for instance, to the case in which the fluid in motion entirely fills a container of constant shape.
In the Eulerian representation, we will denote the density by ? = ?( x, t), the volume forces by f = f ( x, t), and the surface forces applied to the boundary ? ? t of ? t by F = F( x, t). We change our notation and, from now on, we denote the velocity in the Eulerian representation by u = u( x, t) instead of U( x, t); u( x, t) is then the velocity of...
