Decay of solutions to a new Hall–MHD system in $ {\mathbb{R}}^{3}$

Xiaopeng Zhao

doi:10.1016/j.crma.2017.01.019

Partial differential equations

Decay of solutions to a new Hall–MHD system in

R^{3}

Presented by: the Editorial Board

Xiaopeng Zhao ^1,²

¹ Department of Mathematics, Southeast University, Nanjing 210018, China
² School of Science, Jiangnan University, Wuxi 214122, China

Comptes Rendus. Mathématique, Volume 355 (2017) no. 3, pp. 310-317.

Abstract
Résumé

This paper discusses the large-time behavior of solutions for a new Hall–MHD system in $R^{3}$ . Using the Fourier splitting method, we establish the upper bound of the time-decay rate in $L^{2} (R^{3})$ for weak solutions.

Cette Note traite du comportement à long terme des solutions d'un nouveau système d'équations magnétohydrodynamiques de Hall dans $R^{3}$ . Utilisant la méthode de décomposition de Fourier, nous donnons une borne supérieure du taux de décroissance en temps dans $L^{2} (R^{3})$ pour les solutions faibles.

Received: 2016-08-30
Accepted: 2017-01-26
Published online: 2017-02-11

DOI: 10.1016/j.crma.2017.01.019

Author's affiliations:

Xiaopeng Zhao ^{1, 2}

¹ Department of Mathematics, Southeast University, Nanjing 210018, China
² School of Science, Jiangnan University, Wuxi 214122, China

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     author = {Xiaopeng Zhao},
     title = {Decay of solutions to a new {Hall{\textendash}MHD} system in $ {\mathbb{R}}^{3}$},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {310--317},
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     doi = {10.1016/j.crma.2017.01.019},
     language = {en},
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Xiaopeng Zhao. Decay of solutions to a new Hall–MHD system in $ {\mathbb{R}}^{3}$. Comptes Rendus. Mathématique, Volume 355 (2017) no. 3, pp. 310-317. doi : 10.1016/j.crma.2017.01.019. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.01.019/

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