The Non-relativistic Limit of the Euler Nordstr\"om System with Cosmological Constant

TL;DR

This paper analyzes the limit of the Euler-Nordstr"om system as the speed of light approaches infinity, demonstrating convergence to the Euler-Poisson system with a cosmological constant using Sobolev estimates.

Contribution

It develops Sobolev estimates and employs Christodoulou's techniques to rigorously prove the non-relativistic limit of the Euler-Nordstr"om system with a cosmological constant.

Findings

Solutions converge uniformly to Euler-Poisson solutions as c approaches infinity.

The analysis applies Sobolev space techniques to establish convergence.

The results hold for initial data in appropriate Sobolev spaces.

Abstract

In this paper the author studies the singular limit c to infinity of the family of Euler-Nordstr\"om systems indexed by the parameters kappa and c (EN_kappa,c), where kappa^2 > 0 is the cosmological constant and c is the speed of light. Using Christodoulou's techniques to generate energy currents, the author develops Sobolev estimates that show that for initial data belonging to an appropriate Sobolev space, as c tends to infinity, the solutions to the EN_kappa,c system converge uniformly on a spacetime slab [0,T]xR^3 to the solution of the Euler-Poisson system with the cosmological constant kappa^2.