Long time dynamics of nonequilibrium electroconvection

IF 1.2 2区数学 Q1 MATHEMATICS

Transactions of the American Mathematical Society Pub Date : 2024-03-13 DOI:10.1090/tran/9171

Fizay-Noah Lee

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引用次数: 0

Abstract

The Nernst-Planck-Stokes (NPS) system models electroconvection of ions in a fluid. We consider the system, for two oppositely charged ionic species, on three dimensional bounded domains with Dirichlet boundary conditions for the ionic concentrations (modelling ion selectivity), Dirichlet boundary conditions for the electrical potential (modelling an applied potential), and no-slip boundary conditions for the fluid velocity. In this paper, we obtain quantitative bounds on solutions of the NPS system in the long time limit, which we use to prove (1) the existence of a compact global attractor with finite fractal (box-counting) dimension and (2) space-time averaged electroneutrality ρ ≈ 0 \rho \approx 0 in the singular limit of Debye length going to zero, ϵ → 0 \epsilon \to 0 .

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非平衡电对流的长时间动力学

内斯特-普朗克-斯托克斯（NPS）系统是流体中离子电对流的模型。我们考虑的是两个带相反电荷的离子物种在三维有界域上的系统，离子浓度的边界条件为狄里希勒（Dirichlet）（模拟离子选择性），电势的边界条件为狄里希勒（Dirichlet）（模拟外加电势），流体速度的边界条件为无滑动（no-slip）。在本文中，我们获得了 NPS 系统解在长时限内的定量边界，并利用这些边界证明了：（1）存在具有有限分形（盒数）维度的紧凑全局吸引子；（2）在德拜长度为零的奇异极限内，ϵ → 0 \epsilon \to 0 的时空平均电中性 ρ ≈ 0 \rho \approx 0。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Transactions of the American Mathematical Society 数学-数学

CiteScore

2.30

自引率

7.70%

发文量

171

审稿时长

3-6 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to research articles in all areas of pure and applied mathematics. To be published in the Transactions, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Papers of less than 15 printed pages that meet the above criteria should be submitted to the Proceedings of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.