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Global Existence and Temporal Decay of Large Solutions for the Poisson--Nernst--Planck Equations in Low Regularity Spaces
  • Jihong Zhao,
  • Xilan Liu
Jihong Zhao
Baoji University of Arts and Sciences

Corresponding Author:jihzhao@163.com

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Xilan Liu
Baoji University of Arts and Sciences
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Abstract

We are concerned with the global existence and decay rates of large solutions for the Poisson--Nernst--Planck equations. Based on careful observation of algebraic structure of the equations and using the weighted Chemin--Lerner type norm, we obtain the global existence and optimal decay rates of large solutions without requiring the summation of initial densities of a negatively and positively charged species is small enough. Moreover, the large solution is obtained for initial data belonging to the low regularity Besov spaces with different regularity and integral indices for the different charged species, which indicates more specific coupling relations between the negatively and positively charged species.
02 Dec 2021Submitted to Mathematical Methods in the Applied Sciences
04 Dec 2021Submission Checks Completed
04 Dec 2021Assigned to Editor
18 Dec 2021Reviewer(s) Assigned
18 Mar 2022Review(s) Completed, Editorial Evaluation Pending
21 Mar 2022Editorial Decision: Revise Minor
24 Mar 20221st Revision Received
25 Mar 2022Submission Checks Completed
25 Mar 2022Assigned to Editor
25 Mar 2022Reviewer(s) Assigned
28 Mar 2022Review(s) Completed, Editorial Evaluation Pending
19 Jul 2022Editorial Decision: Accept
30 Jan 2023Published in Mathematical Methods in the Applied Sciences volume 46 issue 2 on pages 1667-1686. 10.1002/mma.8599