Existence and optimal decay rates of the compressible non-isentropic Navier-Stokes-Poisson models with external forces

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• 作者：Zhiyuan Zhao ; Yeping Li
• 关键词：35M20 ; 35Q35 ; 76W05
• 刊名：Nonlinear Analysis
• 出版年：2012
• 出版时间：November, 2012
• 年：2012
• 卷：75
• 期：16
• 页码：6130-6147
• 全文大小：295 K

文摘

In this paper, we consider the three dimensional compressible non-isentropic Navier-Stokes-Poisson equations with the potential external force. Under the smallness assumption of the external force in some Sobolev space, the existence of the stationary solution is established by solving a nonlinear elliptic system. Next, we show global well-posedness of the initial value problem for the three dimensional compressible non-isentropic Navier-Stokes-Poisson equations, provided the prescribed initial data is close to the stationary solution. Finally, based on the elaborate energy estimates for the nonlinear system and -decay estimates for the semigroup generated by the linearized equation, we give the optimal -convergence rates of the solutions toward the stationary solution.