Global classical solution of the fractional Nernst-Planck-Poisson-Navier- Stokes system in $ \mathbb{R}^{3} $

Zihang Cai; Chao Jiang; Yuzhu Lei; Zuhan Liu; Zihang Cai; Chao Jiang; Yuzhu Lei; Zuhan Liu

doi:10.3934/math.2024844

AIMS Mathematics

2024, Volume 9, Issue 7: 17359-17385. doi: 10.3934/math.2024844

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Research article

Global classical solution of the fractional Nernst-Planck-Poisson-Navier- Stokes system in $ \mathbb{R}^{3} $

School of Mathematical Science, Yangzhou University, Yangzhou, Jiangsu, 225002, China

Received: 28 March 2024 Revised: 05 May 2024 Accepted: 10 May 2024 Published: 20 May 2024
MSC : 35A01, 35A09, 35Q92, 76D05

In this paper, we consider a fractional Nernst-Planck-Poisson-Navier-Stokes system in $ \mathbb{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.
- Nernst-Planck-Poisson-Navier-Stokes,
- energy estimates,
- fractional diffusion,
- iterative solution sequence,
- global classical solution
Citation: Zihang Cai, Chao Jiang, Yuzhu Lei, Zuhan Liu. Global classical solution of the fractional Nernst-Planck-Poisson-Navier- Stokes system in $ \mathbb{R}^{3} $[J]. AIMS Mathematics, 2024, 9(7): 17359-17385. doi: 10.3934/math.2024844

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Abstract

In this paper, we consider a fractional Nernst-Planck-Poisson-Navier-Stokes system in $ \mathbb{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.

References

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