Analyticity estimates for the 3D magnetohydrodynamic equations

Wenjuan Liu; Jialing Peng; Wenjuan Liu; Jialing Peng

doi:10.3934/era.2024173

Electronic Research Archive

2024, Volume 32, Issue 6: 3819-3842. doi: 10.3934/era.2024173

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Research article

Analyticity estimates for the 3D magnetohydrodynamic equations

Wenjuan Liu ^{1
,
,},
Jialing Peng ²

1.
School of Mathematics, Northwest University, Xi'an 710069, China
2.
School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China

Received: 27 February 2024 Revised: 17 May 2024 Accepted: 22 May 2024 Published: 11 June 2024

This paper was concerned with the Cauchy problem of the 3D magnetohydrodynamic (MHD) system. We first proved that this system was local well-posed with initial data in the Besov space $ \dot{B}^{s}_{p, q}(\mathbb{R}^{3}) $, in the critical Besov space $ \dot{B}^{-1+\frac{3}{p}}_{p, q}(\mathbb{R}^{3}) $, and in $ L^{p}(\mathbb{R}^{3}) $ with $ p\in]3, 6[ $, respectively. We also obtained a new growth rate estimates for the analyticity radius.
- magnetohydrodynamic equations,
- the analyticity radius,
- Besov spaces,
- Gevrey regularity,
- global solution
Citation: Wenjuan Liu, Jialing Peng. Analyticity estimates for the 3D magnetohydrodynamic equations[J]. Electronic Research Archive, 2024, 32(6): 3819-3842. doi: 10.3934/era.2024173

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Abstract

This paper was concerned with the Cauchy problem of the 3D magnetohydrodynamic (MHD) system. We first proved that this system was local well-posed with initial data in the Besov space $ \dot{B}^{s}_{p, q}(\mathbb{R}^{3}) $, in the critical Besov space $ \dot{B}^{-1+\frac{3}{p}}_{p, q}(\mathbb{R}^{3}) $, and in $ L^{p}(\mathbb{R}^{3}) $ with $ p\in]3, 6[ $, respectively. We also obtained a new growth rate estimates for the analyticity radius.

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