THE EXISTENCE AND STABILITY OF STATIONARY SOLUTIONS OF THE INFLOW PROBLEM FOR FULL COMPRESSIBLE NAVIER-STOKES-POISSON SYSTEM

doi:10.1007/s10473-021-0119-z

数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (1): 319-336.doi: 10.1007/s10473-021-0119-z

THE EXISTENCE AND STABILITY OF STATIONARY SOLUTIONS OF THE INFLOW PROBLEM FOR FULL COMPRESSIBLE NAVIER-STOKES-POISSON SYSTEM

Hakho HONG

Institute of Mathematics, State Academy of Sciences, Pyongyang, D P R Korea

收稿日期:2019-06-21 修回日期:2020-07-24 出版日期:2021-02-25 发布日期:2021-04-06
作者简介:Hakho HONG,E-mail:hhong@amss.ac.cn

THE EXISTENCE AND STABILITY OF STATIONARY SOLUTIONS OF THE INFLOW PROBLEM FOR FULL COMPRESSIBLE NAVIER-STOKES-POISSON SYSTEM

Hakho HONG

Institute of Mathematics, State Academy of Sciences, Pyongyang, D P R Korea

Received:2019-06-21 Revised:2020-07-24 Online:2021-02-25 Published:2021-04-06
About author:Hakho HONG,E-mail:hhong@amss.ac.cn

摘要/Abstract

摘要： In this paper, we consider an inflow problem for the non-isentropic Navier-Stokes-Poisson system in a half line (0,∞). For the general gas including ideal polytropic gas, we first give some results for the existence of the stationary solution with the aid of center manifold theory on a 4×4 system of autonomous ordinary differential equations. We also show the time asymptotic stability of the stationary solutions with small strength under smallness assumptions on the initial perturbations by using an elementary energy method.

关键词: Navier-Stokes-Poisson system, inflow problem, stationary solution, existence, stability

Abstract: In this paper, we consider an inflow problem for the non-isentropic Navier-Stokes-Poisson system in a half line (0,∞). For the general gas including ideal polytropic gas, we first give some results for the existence of the stationary solution with the aid of center manifold theory on a 4×4 system of autonomous ordinary differential equations. We also show the time asymptotic stability of the stationary solutions with small strength under smallness assumptions on the initial perturbations by using an elementary energy method.

Key words: Navier-Stokes-Poisson system, inflow problem, stationary solution, existence, stability

中图分类号:

35Q30

Hakho HONG. THE EXISTENCE AND STABILITY OF STATIONARY SOLUTIONS OF THE INFLOW PROBLEM FOR FULL COMPRESSIBLE NAVIER-STOKES-POISSON SYSTEM[J]. 数学物理学报(英文版), 2021, 41(1): 319-336.

Hakho HONG. THE EXISTENCE AND STABILITY OF STATIONARY SOLUTIONS OF THE INFLOW PROBLEM FOR FULL COMPRESSIBLE NAVIER-STOKES-POISSON SYSTEM[J]. Acta mathematica scientia,Series B, 2021, 41(1): 319-336.

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THE EXISTENCE AND STABILITY OF STATIONARY SOLUTIONS OF THE INFLOW PROBLEM FOR FULL COMPRESSIBLE NAVIER-STOKES-POISSON SYSTEM

THE EXISTENCE AND STABILITY OF STATIONARY SOLUTIONS OF THE INFLOW PROBLEM FOR FULL COMPRESSIBLE NAVIER-STOKES-POISSON SYSTEM

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