STRONG SOLUTION FOR BIPOLAR COMPRESSIBLE NAVIER-STOKES-POISSON SYSTEM WITH UNEQUAL VISCOSITIES IN $L^P$-FRAMEWORK

doi:10.1007/s10473-025-0315-3

数学物理学报(英文版) ›› 2025, Vol. 45 ›› Issue (3): 1019-1044.doi: 10.1007/s10473-025-0315-3

STRONG SOLUTION FOR BIPOLAR COMPRESSIBLE NAVIER-STOKES-POISSON SYSTEM WITH UNEQUAL VISCOSITIES IN $L^P$-FRAMEWORK

Zhigang WU¹, Fuyi XU^2,†

1. School of Mathematics and Statistics, Donghua University, Shanghai 201620, China;
2. School of Mathematics and Statistics, Shandong University of Technology, Shandong 255049, China

收稿日期:2023-10-25 修回日期:2024-03-14 出版日期:2025-05-25 发布日期:2025-09-30

STRONG SOLUTION FOR BIPOLAR COMPRESSIBLE NAVIER-STOKES-POISSON SYSTEM WITH UNEQUAL VISCOSITIES IN $L^P$-FRAMEWORK

Zhigang WU¹, Fuyi XU^2,†

1. School of Mathematics and Statistics, Donghua University, Shanghai 201620, China;
2. School of Mathematics and Statistics, Shandong University of Technology, Shandong 255049, China

Received:2023-10-25 Revised:2024-03-14 Online:2025-05-25 Published:2025-09-30
Contact: ^†Fuyi XU, E-mail: zbxufuyi@163.com
About author:Zhigang WU, E-mail: zhigangwu@hotmail.com
Supported by:
Zhigang Wu was supported by the National Natural Science Foundation of China (Grant No. 11971100) and the Natural Science Foundation of Shanghai (Grant No. 22ZR1402300). Fuyi Xu was supported by the National Natural Science Foundation of China (Grant No. 12326430) and the Natural Science Foundation of Shandong Province (Grant No. ZR2021MA017).

摘要/Abstract

摘要： The present paper deals with the Cauchy problem to a two-fluid plasma model with unequal viscosities in any dimension $N\geq2$. Employing the precise spectral analysis for the corresponding linearized system, we prove the global well-posedness provided that the initial data are close to a stable equilibrium state in critical functional framework which is not related to the energy space. Moreover, the optimal decay rates for the constructed global solution are also established.

关键词: bipolar, Navier-Stokes-Poission system, unequal viscosities, global well-posedness, optimal decay rates

Abstract: The present paper deals with the Cauchy problem to a two-fluid plasma model with unequal viscosities in any dimension $N\geq2$. Employing the precise spectral analysis for the corresponding linearized system, we prove the global well-posedness provided that the initial data are close to a stable equilibrium state in critical functional framework which is not related to the energy space. Moreover, the optimal decay rates for the constructed global solution are also established.

Key words: bipolar, Navier-Stokes-Poission system, unequal viscosities, global well-posedness, optimal decay rates

中图分类号:

76W05

Zhigang WU, Fuyi XU. STRONG SOLUTION FOR BIPOLAR COMPRESSIBLE NAVIER-STOKES-POISSON SYSTEM WITH UNEQUAL VISCOSITIES IN $L^P$-FRAMEWORK[J]. 数学物理学报(英文版), 2025, 45(3): 1019-1044.

Zhigang WU, Fuyi XU. STRONG SOLUTION FOR BIPOLAR COMPRESSIBLE NAVIER-STOKES-POISSON SYSTEM WITH UNEQUAL VISCOSITIES IN $L^P$-FRAMEWORK[J]. Acta mathematica scientia,Series B, 2025, 45(3): 1019-1044.

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STRONG SOLUTION FOR BIPOLAR COMPRESSIBLE NAVIER-STOKES-POISSON SYSTEM WITH UNEQUAL VISCOSITIES IN $L^P$-FRAMEWORK

STRONG SOLUTION FOR BIPOLAR COMPRESSIBLE NAVIER-STOKES-POISSON SYSTEM WITH UNEQUAL VISCOSITIES IN $L^P$-FRAMEWORK

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