The stability of stationary solution for outflow problem on the navier-stokes-poisson system

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• 作者：Mina JIANG^a ; ^{jmn3911@mail.ccnu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Suhua LAI^b ; ^{ccnulaisuhua@163.com" class="auth_mail" title="E-mail the corresponding author} ; Haiyan YIN^c ; ^{yinhaiyan2000@aliyun.com" class="auth_mail" title="E-mail the corresponding author} ; Changjiang ZHU^d ; ^{machjzhu@scut.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Navier-Stokes-Poisson system ; stationary solution ; outflow problem ; convergence rate ; weighted energy method
• 刊名：Acta Mathematica Scientia
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：36
• 期：4
• 页码：1098-1116
• 全文大小：320 K

文摘

In this article, we are concerned with the stability of stationary solution for outflow problem on the Navier-Stokes-Poisson system. We obtain the unique existence and the asymptotic stability of stationary solution. Moreover, the convergence rate of solution towards stationary solution is obtained. Precisely, if an initial perturbation decays with the algebraic or the exponential rate in space, the solution converges to the corresponding stationary solution as time tends to infinity with the algebraic or the exponential rate in time. The proof is based on the weighted energy method by taking into account the effect of the self-consistent electric field on the viscous compressible fluid.