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The stability for stationary solution of Euler-Poisson equations. (Chinese. English summary) Zbl 1340.35243

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
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