Global Existence for the N Body Euler-Poisson System

TL;DR

This paper proves the existence of global-in-time solutions for multiple expanding stars interacting gravitationally, demonstrating conditions under which they avoid collision despite mutual attraction.

Contribution

It introduces a novel scaling approach and detailed analysis to establish global solutions for the N Body Euler-Poisson system with gravitational interactions.

Findings

Large class of initial conditions lead to collision-free expansion

Scaling mechanism effectively handles gravitational effects

Provides mathematical proof of global existence for expanding stars

Abstract

In this paper we investigate the problem of multiple expanding Newtonian stars that interact via their gravitational effect on each other. It is clear physically that if two stars at rest are separated initially, and start expanding as well as moving according to the laws of Newtonian gravity, they may eventually collide. Thus, one can ask whether each star can be given an initial position and velocity such that they can keep expanding without touching. We show that even with gravitational interaction between the bodies, a large class of initial positions and velocities give global-in-time solutions to the N Body Euler-Poisson system. To do this we use a scaling mechanism present in the compressible Euler system shown in [63] and a careful analysis of how the gravitational interaction between stars affects their dynamics.