Energy conservation for the compressible ideal Hall-MHD equations

Yanping Zhou; Xuemei Deng; Qunyi Bie; Lingping Kang; Yanping Zhou; Xuemei Deng; Qunyi Bie; Lingping Kang

doi:10.3934/math.2022944

AIMS Mathematics

2022, Volume 7, Issue 9: 17150-17165. doi: 10.3934/math.2022944

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Research article

Energy conservation for the compressible ideal Hall-MHD equations

1.
College of Science & Three Gorges Mathematical Research Center, China Three Gorges University, Yichang 443002, China
2.
College of Science, China Three Gorges University, Yichang 443002, China

Received: 13 May 2022 Revised: 03 July 2022 Accepted: 18 July 2022 Published: 21 July 2022
MSC : 35B65, 35D30, 35Q35, 76W05

In this paper, we study the regularity and energy conservation of the weak solutions for compressible ideal Hall-magnetohydrodynamic (Hall-MHD) system, where $ (t, x)\in(0, T)\times {\mathbb{T}}^d(d\geq\; 1) $. By exploring the special structure of the nonlinear terms in the model, we obtain the sufficient conditions for the regularity of the weak solutions for energy conservation. Our main strategy relies on commutator estimates.
- compressible ideal Hall-MHD system,
- regularity,
- energy conservation
Citation: Yanping Zhou, Xuemei Deng, Qunyi Bie, Lingping Kang. Energy conservation for the compressible ideal Hall-MHD equations[J]. AIMS Mathematics, 2022, 7(9): 17150-17165. doi: 10.3934/math.2022944

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Abstract

In this paper, we study the regularity and energy conservation of the weak solutions for compressible ideal Hall-magnetohydrodynamic (Hall-MHD) system, where $ (t, x)\in(0, T)\times {\mathbb{T}}^d(d\geq\; 1) $. By exploring the special structure of the nonlinear terms in the model, we obtain the sufficient conditions for the regularity of the weak solutions for energy conservation. Our main strategy relies on commutator estimates.

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