  The system consisting of a self gravitating perfect fluid and scalar field is
considered in detail. The scalar fields considered are the quintessence and
``tachyonic'' forms which have important application in cosmology. Mathematical
properties of the general system of equations are studied including the
algebraic and differential identities as well as the eigenvalue structure. The
Cauchy problem for both quintessence and the tachyon is presented. We discuss
the initial constraint equations which must be satisfied by the initial data. A
Cauchy evolution scheme is presented in the form of a Taylor series about the
Cauchy surface. Finally, a simple numerical example is provided to illustrate
this scheme.
