THE TIME DECAY RATES OF THE CLASSICAL SOLUTION TO THE POISSON-NERNST-PLANCK-FOURIER EQUATIONS IN $\mathbb{R}^3$

doi:10.1007/s10473-022-0315-5

数学物理学报(英文版) ›› 2022, Vol. 42 ›› Issue (3): 1081-1102.doi: 10.1007/s10473-022-0315-5

THE TIME DECAY RATES OF THE CLASSICAL SOLUTION TO THE POISSON-NERNST-PLANCK-FOURIER EQUATIONS IN $\mathbb{R}^3$

童雷雷¹, 谭忠², 张旭³

1. School of Science, Chongqing University of Posts and Telecommunications, Chongqing, 400065, China;
2. School of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling & High Performance Scientific Computing, Xiamen University, Xiamen, 361005, China;
3. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, 450001, China

收稿日期:2020-11-18 修回日期:2021-04-08 发布日期:2022-06-24
通讯作者: Xu ZHANG,E-mail:xuzhang889@zzu.edu.cn E-mail:xuzhang889@zzu.edu.cn
基金资助:
The work of the first author was supported by the National Natural Science Foundation of China (12001077), the Science and Technology Research Program of Chongqing Municipal Education Commission (KJQN202000618) and Chongqing University of Posts and Telecommunications startup fund (A2018-128). The second author was supported by the National Natural Science Foundation of China (11926316, 11531010). The third author was supported by National Natural Science Foundation of China (11901537).

THE TIME DECAY RATES OF THE CLASSICAL SOLUTION TO THE POISSON-NERNST-PLANCK-FOURIER EQUATIONS IN $\mathbb{R}^3$

Leilei TONG¹, Zhong TAN², Xu ZHANG³

1. School of Science, Chongqing University of Posts and Telecommunications, Chongqing, 400065, China;
2. School of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling & High Performance Scientific Computing, Xiamen University, Xiamen, 361005, China;
3. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, 450001, China

Received:2020-11-18 Revised:2021-04-08 Published:2022-06-24
Contact: Xu ZHANG,E-mail:xuzhang889@zzu.edu.cn E-mail:xuzhang889@zzu.edu.cn
Supported by:
The work of the first author was supported by the National Natural Science Foundation of China (12001077), the Science and Technology Research Program of Chongqing Municipal Education Commission (KJQN202000618) and Chongqing University of Posts and Telecommunications startup fund (A2018-128). The second author was supported by the National Natural Science Foundation of China (11926316, 11531010). The third author was supported by National Natural Science Foundation of China (11901537).

摘要/Abstract

摘要： In this work, the Poisson-Nernst-Planck-Fourier system in three dimensions is considered. For when the initial data regards a small perturbation around the constant equilibrium state in a $H^3\cap\dot{H}^{-s} (0\leq s\leq 1/2)$ norm, we obtain the time convergence rate of the global solution by a regularity interpolation trick and an energy method.

关键词: Poisson-Nernst-Planck-Fourier system, decay rates, energy method

Abstract: In this work, the Poisson-Nernst-Planck-Fourier system in three dimensions is considered. For when the initial data regards a small perturbation around the constant equilibrium state in a $H^3\cap\dot{H}^{-s} (0\leq s\leq 1/2)$ norm, we obtain the time convergence rate of the global solution by a regularity interpolation trick and an energy method.

Key words: Poisson-Nernst-Planck-Fourier system, decay rates, energy method

中图分类号:

35Q70

童雷雷, 谭忠, 张旭. THE TIME DECAY RATES OF THE CLASSICAL SOLUTION TO THE POISSON-NERNST-PLANCK-FOURIER EQUATIONS IN $\mathbb{R}^3$[J]. 数学物理学报(英文版), 2022, 42(3): 1081-1102.

Leilei TONG, Zhong TAN, Xu ZHANG. THE TIME DECAY RATES OF THE CLASSICAL SOLUTION TO THE POISSON-NERNST-PLANCK-FOURIER EQUATIONS IN $\mathbb{R}^3$[J]. Acta mathematica scientia,Series B, 2022, 42(3): 1081-1102.

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THE TIME DECAY RATES OF THE CLASSICAL SOLUTION TO THE POISSON-NERNST-PLANCK-FOURIER EQUATIONS IN $\mathbb{R}^3$

THE TIME DECAY RATES OF THE CLASSICAL SOLUTION TO THE POISSON-NERNST-PLANCK-FOURIER EQUATIONS IN $\mathbb{R}^3$

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