Abstract 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 R2 with possible applications to the formation of plate, spiral galaxies and the evolution of gas-rich, disk-like galaxies. The results complement Yuen's solutions without rotation (Yuen, 2008 ). 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 Weber's solutions are conjectured.