Global Existence for the N Body Euler–Poisson System

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 if two at rest are separated initially, and start as well moving according to laws gravity, they may eventually collide. Thus, one can ask whether star be given an initial position velocity such keep without touching. We show even with interaction between bodies, a large class positions velocities give global-in-time solutions N Body Euler–Poisson system. To do use scaling mechanisms present in compressible Euler system, shown Parmeshwar (Quart Appl Math 79(2):273–334, 2021), gaining advantageous time weights smallness our estimates under specific form Lagrangian flow maps, assumption small mass for star, represented by parameter $$\delta $$ δ . This combined careful analysis how affects dynamics.