Acta mathematica scientia,Series B ›› 2022, Vol. 42 ›› Issue (3): 1081-1102.doi: 10.1007/s10473-022-0315-5

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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. 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).

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

CLC Number: 

  • 35Q70
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