Periodic solutions of 2D isothermal Euler–Poisson equations with possible applications to spiral and disk-like galaxies

Compressible Euler–Poisson equations are the standard self-gravitating models for stellar dynamics in classical astrophysics. In this article, we construct periodic solutions to the isothermal ( γ = 1 ) Euler–Poisson equations in R 2 with possible applications to the formation of plate, spiral galaxies and the evolution of gas-rich, disk-like galaxies. The results complement Yuenʹs solutions without rotation (Yuen, 2008 [12]). Here, the periodic rotation prevents the blowup phenomena that occur in solutions without rotation. Based on our results, the corresponding 3D rotational results for Goldreich and Weberʹs solutions are conjectured.