论泊松-恩斯特-普朗克-纳维尔-斯托克斯系统解的良好拟合和衰减率

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-04-25 DOI:10.1007/s00021-024-00867-2

Xiaoping Zhai, Zhigang Wu

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引用次数: 0

摘要

我们考虑与 Poisson-Nernst-Planck-Navier-Stokes 系统相关的初值问题，该问题由 Wang 等人（J Differ Equ 262:68-115, 2017）通过能量变分法（EVA）首次得出。利用谐波分析工具（尤其是 Littlewood-Paley 理论），我们首先研究了该系统在临界 Besov 空间中的局部和全局好摆性。然后，在一个只涉及初始数据低频的适当条件下，我们利用能量函数的 Lyapunov 型不等式，为所构建的全局解建立最佳时间衰减率。证明的关键取决于对负（正）电荷分布的额外影响和非标准乘积估计、插值不等式的仔细分析。

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On the Well-Posedness and Decay Rates of Solutions to the Poisson–Nernst–Planck–Navier–Stokes System

We consider the initial value problem associated to the Poisson–Nernst–Planck–Navier–Stokes system which is first derived by Wang et al. (J Differ Equ 262:68–115, 2017) through an Energetic Variational Approach (EVA). Exploiting harmonic analysis tools (especially Littlewood–Paley theory), we first study the local and global well-posedness of the system in critical Besov spaces. Then, under a suitable condition involving only low-frequency of initial data, we use the Lyapunov-type inequality of the energy functionals to establish optimal time decay rates for the constructed global solutions. The proof crucially depends on a careful analysis for treating the extra effect of the distribution for the negative (positive) charge and non-standard product estimates, interpolation inequalities.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.