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Research Article | Open Access

Global classical solution of the fractional Nernst-Planck-Poisson-Navier- Stokes system in R 3

Zihang Cai, Chao Jiang, Yuzhu Lei( ), Zuhan Liu
School of Mathematical Science, Yangzhou University, Yangzhou, Jiangsu, 225002, China
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Abstract

In this paper, we consider a fractional Nernst-Planck-Poisson-Navier-Stokes system in R 3 . First, we obtain a priori estimates by using energy estimates. Then, we construct an iterative solution sequence by solving the approximate problem and obtaining the local existence and uniqueness of the classical solution. Finally, combining the local existence with a priori estimates, the global existence and uniqueness of the classical solution with small initial data are obtained.

Keywords

Nernst-Planck-Poisson-Navier-Stokesenergy estimatesfractional diffusioniterative solution sequenceglobal classical solution
CLC number: 35A01, 35A09, 35Q92, 76D05

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AIMS Mathematics
Volume 9 Issue 7,
July 2024
Pages 17359-17385
DOI: 10.3934/math.2024844

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Cite this article:
Cai Z, Jiang C, Lei Y, et al. Global classical solution of the fractional Nernst-Planck-Poisson-Navier- Stokes system in R 3 . AIMS Mathematics, 2024, 9(7): 17359-17385. https://doi.org/10.3934/math.2024844

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Received: 28 March 2024
Revised: 05 May 2024
Accepted: 10 May 2024
Published: 15 July 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)