The Non-relativistic Limit of the Euler Nordström System with Cosmological Constant

Abstract

In this paper the author studies the singular limit c to infinity of the family of Euler-Nordström 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.

Some minor typos were corrected. Page formatting changed to resemble that of the published version. 57 pages

References in corpus (3)

• Global classical solutions to the 3D Nordström-Vlasov system
• The Newtonian limit for perfect fluids
• Multipole radiation in a collisonless gas coupled to electromagnetism or scalar gravitation

Cited by in corpus (4)

• Hilbert Expansion from the Boltzmann equation to relativistic Fluids
• The Stabilizing Effect of Spacetime Expansion on Relativistic Fluids With Sharp Results for the Radiation Equation of State
• The Nonlinear Stability of the Trivial Solution to the Maxwell-Born-Infeld System
• The Global Stability of the Minkowski Spacetime Solution to the Einstein-Nonlinear Electromagnetic System in Wave Coordinates