## – Europe/Lisbon — Online

Shrish Parmeshwar, University of Bath

Global-in-Time Solutions to the N-Body Euler-Poisson System

We investigate the $N$-Body compressible Euler-Poisson system, modelling multiple stars interacting with each other via Newtonian gravity. If we prescribe initial data so that each star expands indefinitely, one might expect that two of them will collide in finite time due to their expansion, and the influence of gravity. In this talk we show that there exists a large family of initial positions and velocities for the system such that each star can expand for all time, but no two will touch in finite time. To do this we use scaling mechanisms present in the compressible Euler system, and a careful analysis of how the gravitational interaction between stars affects their dynamics.