Global Existence for the N Body Euler–Poisson System

Abstract

AbstractIn 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 scaling mechanisms present in the compressible Euler system, shown in Parmeshwar (Quart Appl Math 79(2):273–334, 2021), gaining advantageous time weights and smallness in our estimates under the specific form of the Lagrangian flow maps, and assumption of small mass for each star, represented by a parameter $$\delta $$ δ . This is combined with a careful analysis of how the gravitational interaction between stars affects their dynamics.