From Classical Continuum Theory to Euler Equations via N-S-F Equations

Abstract

In classical continuum theory, we relate field variables by specific axioms called constitutive relations. For an elementary introduction to the basic concepts and assumptions of continuum mechanics, the reader may consult Truesdell (1977). Many materials are homogeneous in the sense that each part of the material has the same response to a given set of stimuli as all of the other parts. An example of such a material is pure water. Formulation of equations that describe the behavior of homogeneous materials is well understood and is described in numerous standard textbooks (see, for instance, Gurtin, 1981). We expect the reader of this book to have sufficient background to follow our use of classical results in continuum mechanics. The short introduction to the subject we give here is intended only to fix notation and our basic ideas. Our intent is not to condense all of the knowledge about continuum mechanics into a few pages. Rather, we present the material we will use in later chapter.