LARGE TIME BEHAVIOR OF THE 1D ISENTROPIC NAVIER-STOKES-POISSON SYSTEM

doi:10.1007/s10473-022-0509-x

数学物理学报(英文版) ›› 2022, Vol. 42 ›› Issue (5): 1843-1874.doi: 10.1007/s10473-022-0509-x

• 论文 • 上一篇

LARGE TIME BEHAVIOR OF THE 1D ISENTROPIC NAVIER-STOKES-POISSON SYSTEM

Qingyou He¹, Jiawei Sun²

1. Department of Mathematics, Capital Normal University, Beijing, 100048, China;
2. Department of Mathematics, Shandong Normal University, Jinan, 250014, China

收稿日期:2021-03-07 修回日期:2022-05-19 发布日期:2022-11-02
通讯作者: Jiawei Sun,E-mail:sunjiawei0122@163.com E-mail:sunjiawei0122@163.com
基金资助:
The research was supported by National Natural Science Foundation of China (11931010, 11671384, 11871047 and 12101372) and by the key research project of Academy for Multidisciplinary Studies, Capital Normal University, and by the Capacity Building for Sci-Tech InnovationFundamental Scientific Research Funds (007/20530290068).

LARGE TIME BEHAVIOR OF THE 1D ISENTROPIC NAVIER-STOKES-POISSON SYSTEM

Qingyou He¹, Jiawei Sun²

1. Department of Mathematics, Capital Normal University, Beijing, 100048, China;
2. Department of Mathematics, Shandong Normal University, Jinan, 250014, China

Received:2021-03-07 Revised:2022-05-19 Published:2022-11-02
Contact: Jiawei Sun,E-mail:sunjiawei0122@163.com E-mail:sunjiawei0122@163.com
Supported by:
The research was supported by National Natural Science Foundation of China (11931010, 11671384, 11871047 and 12101372) and by the key research project of Academy for Multidisciplinary Studies, Capital Normal University, and by the Capacity Building for Sci-Tech InnovationFundamental Scientific Research Funds (007/20530290068).

摘要/Abstract

摘要： The initial value problem (IVP) for the one-dimensional isentropic compressible Navier-Stokes-Poisson (CNSP) system is considered in this paper. For the variables, the electric field and the velocity, under the Lagrange coordinate, we establish the global existence and uniqueness of the classical solutions to this IVP problem. Then we prove by the method of complex analysis, that the solutions to this system converge to those of the corresponding linearized system in the L² norm as time tends to infinity. In addition, we show, using Green’s function, that the solutions to this system are close to a diffusion profile, pointwisely, as time goes to infinity.

关键词: 1D Navier-Stokes-Poisson system, well-posedness, L²-time decay rates, time-space pointwise behaviors

Abstract: The initial value problem (IVP) for the one-dimensional isentropic compressible Navier-Stokes-Poisson (CNSP) system is considered in this paper. For the variables, the electric field and the velocity, under the Lagrange coordinate, we establish the global existence and uniqueness of the classical solutions to this IVP problem. Then we prove by the method of complex analysis, that the solutions to this system converge to those of the corresponding linearized system in the L² norm as time tends to infinity. In addition, we show, using Green’s function, that the solutions to this system are close to a diffusion profile, pointwisely, as time goes to infinity.

Key words: 1D Navier-Stokes-Poisson system, well-posedness, L²-time decay rates, time-space pointwise behaviors

中图分类号:

35M10

Qingyou He, Jiawei Sun. LARGE TIME BEHAVIOR OF THE 1D ISENTROPIC NAVIER-STOKES-POISSON SYSTEM[J]. 数学物理学报(英文版), 2022, 42(5): 1843-1874.

Qingyou He, Jiawei Sun. LARGE TIME BEHAVIOR OF THE 1D ISENTROPIC NAVIER-STOKES-POISSON SYSTEM[J]. Acta mathematica scientia,Series B, 2022, 42(5): 1843-1874.

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LARGE TIME BEHAVIOR OF THE 1D ISENTROPIC NAVIER-STOKES-POISSON SYSTEM

LARGE TIME BEHAVIOR OF THE 1D ISENTROPIC NAVIER-STOKES-POISSON SYSTEM

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