Acta mathematica scientia, Series B >
THE STABILITY OF STATIONARY SOLUTION FOR OUTFLOW PROBLEM ON THE NAVIER-STOKES-POISSON SYSTEM
Received date: 2015-07-24
Revised date: 2016-01-24
Online published: 2016-08-25
Supported by
The research was supported by the National Natural Science Foundation of China (11331005, 11471134), the Program for Changjiang Scholars and Innovative Research Team in University (IRT13066), and the Scientific Research Funds of Huaqiao University (15BS201, 15BS309).
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.
Mina JIANG , Suhua LAI , Haiyan YIN , Changjiang ZHU . THE STABILITY OF STATIONARY SOLUTION FOR OUTFLOW PROBLEM ON THE NAVIER-STOKES-POISSON SYSTEM[J]. Acta mathematica scientia, Series B, 2016 , 36(4) : 1098 -1116 . DOI: 10.1016/S0252-9602(16)30058-3
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