Comptes Rendus
no. 3
Partial differential equations
Decay of solutions to a new Hall–MHD system in R3
[Décroissance des solutions d'un nouveau système d'équations magnétohydrodynamiques de Hall dans R3]

Présenté par : the Editorial Board

Xiaopeng Zhao1, 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.

This paper discusses the large-time behavior of solutions for a new Hall–MHD system in R3. Using the Fourier splitting method, we establish the upper bound of the time-decay rate in L2(R3) for weak solutions.

Cette Note traite du comportement à long terme des solutions d'un nouveau système d'équations magnétohydrodynamiques de Hall dans R3. Utilisant la méthode de décomposition de Fourier, nous donnons une borne supérieure du taux de décroissance en temps dans L2(R3) pour les solutions faibles.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2017.01.019

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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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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  • Jae-Myoung Kim Existence, uniqueness and decay rates of a certain type of 3D Hall-MHD equations with power-law type, Analysis and Mathematical Physics, Volume 14 (2024) no. 2 | DOI:10.1007/s13324-024-00882-6
  • Bin Han; Ke Hu; Ning-An Lai On the global well-posedness for the compressible Hall-MHD system, Journal of Mathematical Physics, Volume 65 (2024) no. 1 | DOI:10.1063/5.0175649
  • Shu An; Jing Chen; Bin Han THE GLOBAL STRONG SOLUTIONS OF THE 3D INCOMPRESSIBLE HALL-MHD SYSTEM WITH VARIABLE DENSITY, Mathematical Modelling and Analysis, Volume 29 (2024) no. 2, p. 288 | DOI:10.3846/mma.2024.17776
  • Jae‐Myoung Kim Decay estimates for a class of non‐Newtonian 3D magneto‐micropolar fluids, ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Volume 102 (2022) no. 10 | DOI:10.1002/zamm.202000218
  • Zhaoyang Shang Global existence and large time behavior of solutions for full compressible Hall-MHD equations, Applicable Analysis, Volume 99 (2020) no. 11, p. 1865 | DOI:10.1080/00036811.2018.1549320
  • Xiaopeng Zhao On Global Well-Posedness and Temporal Decay for 3D Magnetic Induction Equations with Hall Effect, Mathematics, Volume 8 (2020) no. 10, p. 1847 | DOI:10.3390/math8101847
  • Xiaopeng Zhao Global well-posedness and decay characterization of solutions to 3D MHD equations with Hall and ion-slip effects, Zeitschrift für angewandte Mathematik und Physik, Volume 71 (2020) no. 3 | DOI:10.1007/s00033-020-01313-9
  • Xiaopeng Zhao Asymptotic Behavior of Solutions to a New Hall-MHD System, Acta Applicandae Mathematicae, Volume 157 (2018) no. 1, p. 205 | DOI:10.1007/s10440-018-0170-5
  • Ning Duan Global well-posedness and analyticity of solutions to three-dimensional Hall-MHD equations, Journal of Mathematical Analysis and Applications, Volume 463 (2018) no. 2, p. 506 | DOI:10.1016/j.jmaa.2018.03.020
  • Xiaopeng Zhao; Mingxuan Zhu Decay characterization of solutions to generalized Hall-MHD system in R3, Journal of Mathematical Physics, Volume 59 (2018) no. 7 | DOI:10.1063/1.5040409
  • Xiaopeng Zhao; Mingxuan Zhu Global well-posedness and asymptotic behavior of solutions for the three-dimensional MHD equations with Hall and ion-slip effects, Zeitschrift für angewandte Mathematik und Physik, Volume 69 (2018) no. 2 | DOI:10.1007/s00033-018-0907-z

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