NotePeriodic 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 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 [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 Weber's solutions are conjectured.