THE NON-RELATIVISTIC LIMIT OF THE EULER–NORDSTRÖM SYSTEM WITH COSMOLOGICAL CONSTANT

Abstract

In this paper, we study the singular limit c → ∞ of the family of Euler–Nordström systems indexed by the parameters κ2 and c[Formula: see text], 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 [Formula: see text] system that converge to corresponding unique solutions of the Euler–Poisson system with the cosmological constant κ2 as c tends to infinity.