Xie, Huazhao; Li, Suli The stability for stationary solution of Euler-Poisson equations. (Chinese. English summary) Zbl 1340.35243 Acta Math. Appl. Sin. 38, No. 4, 619-631 (2015). Summary: In three dimension spaces, the motion of a compressible isentropic perfect gaseous star with self-gravitation is modeled by the Euler-Poisson equations. The main purpose of this paper is concerned with stationary solutions and the nonlinear stability of gaseous stars. Under a case that \(\frac 1{\gamma-1}\int_{\mathbb R^3}\rho^\gamma\text{ d}x=M\) is conserved, with prescribed angular velocity, if \(\frac 65<\gamma<2\), we prove the existence of stationary solution of E-P equations; the nonlinear stability of such steady states is also proved. If \(v\equiv 0\), the support of \(\rho\) is \(B_R(0)\), then the stationary solution of E-P equations is spherically symmetric and unique. MSC: 35Q05 Euler-Poisson-Darboux equations 35B35 Stability in context of PDEs Keywords:gaseous stars; Euler-Poisson equations; stationary solution; nonlinear stability PDFBibTeX XMLCite \textit{H. Xie} and \textit{S. Li}, Acta Math. Appl. Sin. 38, No. 4, 619--631 (2015; Zbl 1340.35243)