Analytical Blowup Solutions to the 2-dimensional Isothermal Euler-Poisson Equations of Gaseous Stars II

TL;DR

This paper constructs new non-radial blowup solutions for the 2D isothermal Euler-Poisson equations, extending previous radial solutions and marking the first known non-radial evolutionary solutions for this system.

Contribution

It introduces novel non-radial blowup solutions for the 2D isothermal Euler-Poisson equations using the separation method, expanding the understanding of solution symmetries.

Findings

First non-radial evolutionary solutions for the system

Extension of radial blowup solutions to non-radial cases

Construction of solutions with line source or sink features

Abstract

This article is the continued version of the analytical blowup solutions for 2-dimensional Euler-Poisson equations \cite{Y1}. With extension of the blowup solutions with radial symmetry for the isothermal Euler-Poisson equations in $R^{2}$, other special blowup solutions in $R^{2}$ with non-radial symmetry are constructed by the separation method. We notice that the results are the first evolutionary solutions with non-radial symmetry for the system. Key words: Analytical Solutions, Euler-Poisson Equations, Isothermal, Blowup, Non-radial Symmetry, Line Source or Sink