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Research Article | Open Access

Energy conservation for the compressible ideal Hall-MHD equations

Yanping Zhou1, Xuemei Deng1, Qunyi Bie1, Lingping Kang2( )
College of Science & Three Gorges Mathematical Research Center, China Three Gorges University, Yichang 443002, China
College of Science, China Three Gorges University, Yichang 443002, China
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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 ) ∈ ( 0 , T ) × T d ( d ≥ 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.

Keywords

compressible ideal Hall-MHD systemregularityenergy conservation
CLC number: 35B65, 35D30, 35Q35, 76W05

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AIMS Mathematics
Volume 7 Issue 9,
September 2022
Pages 17150-17165
DOI: 10.3934/math.2022944

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Cite this article:
Zhou Y, Deng X, Bie Q, et al. Energy conservation for the compressible ideal Hall-MHD equations. AIMS Mathematics, 2022, 7(9): 17150-17165. https://doi.org/10.3934/math.2022944

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Received: 13 May 2022
Revised: 03 July 2022
Accepted: 18 July 2022
Published: 15 September 2022
©2022 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)