Periodic Solutions of 2D Isothermal Euler-Poisson Equations with Possible Applications to Spiral and Disk-like Galaxies

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 ($\gamma =1$) 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 Yuen's solutions without rotation (M.W. Yuen, Analytical Blowup Solutions to the 2-dimensional Isothermal Euler-Poisson Equations of Gaseous Stars, J. Math. Anal. Appl. 341(2008), 445--456.). Here, the periodic rotation prevents the blowup phenomena that occur in solutions without rotation. Based on our results, the corresponding $3$D rotational results for Goldreich and Weber's solutions are conjectured.

12 Pages. Key Words: Euler-Poisson Equations, Periodic Solutions, Rotational Solutions, Galaxies Formation, Galaxies Evolution, Gaseous Stars

References in corpus (4)

• Analytical Blowup Solutions to the 2-dimensional Isothermal Euler-Poisson Equations of Gaseous Stars
• Exact, Rotational, Infinite Energy, Blowup Solutions to the 3-Dimensional Euler Equations
• Analytical Blowup Solutions to the Pressureless Navier-Stokes-Poisson Equations with Density-dependent Viscosity in R^N
• Analytically Periodic Solutions to the 3-dimensional Euler-Poisson Equations of Gaseous Stars with Negative Cosmological Constant