  In this paper the author considers the motion of a relativistic perfect fluid
with self-interaction mediated by Nordstrom's scalar theory of gravity. The
evolution of the fluid is determined by a quasilinear hyperbolic system of
PDEs, and a cosmological constant is introduced in order to ensure the
existence of non-zero constant solutions. Accordingly, the initial value
problem for a compact perturbation of an infinitely extended quiet fluid is
studied. Although the system is neither symmetric hyperbolic nor strictly
hyperbolic, Christodoulou's constructive results on the existence of energy
currents for equations derivable from a Lagrangian can be adapted to provide
energy currents that can be used in place of the standard energy principle
available for first-order symmetric hyperbolic systems. After providing such
energy currents, the author uses them to prove that the Euler-Nordstrom system
with a cosmological constant is well-posed in a suitable Sobolev space.
