Narrow Results

In this paper, we study the singular limit c → ∞ of the family of Euler–Nordström systems indexed by the parameters κ² and c, where κ² > 0 is the cosmological constant and c is the speed of light. Using Christodoulou's techniques to generate energy currents, we develop Sobolev estimates that show initial data belonging to an appropriate Sobolev space launch unique solutions to the system that converge to corresponding unique solutions of the Euler–Poisson system with the cosmological constant κ² as c tends to infinity.

In this paper, the author considers the motion of a relativistic perfect fluid with self-interaction mediated by Nordström'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 nonzero 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–Nordström system with a cosmological constant is well-posed in a suitable Sobolev space.