On the energy method for the global solutions to the three dimensional incompressible non-resistive MHD near equilibrium

Yuan Cai; Bin Han; Na Zhao

doi:10.1063/5.0267433

On the energy method for the global solutions to the three dimensional incompressible non-resistive MHD near equilibrium

Yuan Cai, Bin Han^*, Na Zhao

^*Corresponding author for this work

Research output: Contribution to journal › Journal Article › peer-review

Abstract

We prove the global existence of the smooth solutions near equilibrium to the Cauchy problem of the incompressible non-resistive magnetohydrodynamic equations in the whole three dimensional space. The result has been obtained by Xu and Zhang [SIAM J. Math. Anal. 47, 26-65 (2015)] and by Abidi and Zhang [Commun. Pure Appl. Math. 70, 1509-1561 (2017)] in anisotropic Besov space framework. In this paper, we provide a new proof based on the temporal weighted energy method.

Original language	English
Article number	071501
Journal	Journal of Mathematical Physics
Volume	66
Issue number	7
DOIs	https://doi.org/10.1063/5.0267433
Publication status	Published - 1 Jul 2025
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2025 Author(s).

Access to Document

10.1063/5.0267433

Cite this

@article{6fd579a179e54bfd9c4129176cfc65fd,

title = "On the energy method for the global solutions to the three dimensional incompressible non-resistive MHD near equilibrium",

abstract = "We prove the global existence of the smooth solutions near equilibrium to the Cauchy problem of the incompressible non-resistive magnetohydrodynamic equations in the whole three dimensional space. The result has been obtained by Xu and Zhang [SIAM J. Math. Anal. 47, 26-65 (2015)] and by Abidi and Zhang [Commun. Pure Appl. Math. 70, 1509-1561 (2017)] in anisotropic Besov space framework. In this paper, we provide a new proof based on the temporal weighted energy method.",

author = "Yuan Cai and Bin Han and Na Zhao",

note = "Publisher Copyright: {\textcopyright} 2025 Author(s).",

year = "2025",

month = jul,

day = "1",

doi = "10.1063/5.0267433",

language = "English",

volume = "66",

journal = "Journal of Mathematical Physics",

issn = "0022-2488",

publisher = "American Institute of Physics",

number = "7",

}

TY - JOUR

T1 - On the energy method for the global solutions to the three dimensional incompressible non-resistive MHD near equilibrium

AU - Cai, Yuan

AU - Han, Bin

AU - Zhao, Na

PY - 2025/7/1

Y1 - 2025/7/1

N2 - We prove the global existence of the smooth solutions near equilibrium to the Cauchy problem of the incompressible non-resistive magnetohydrodynamic equations in the whole three dimensional space. The result has been obtained by Xu and Zhang [SIAM J. Math. Anal. 47, 26-65 (2015)] and by Abidi and Zhang [Commun. Pure Appl. Math. 70, 1509-1561 (2017)] in anisotropic Besov space framework. In this paper, we provide a new proof based on the temporal weighted energy method.

AB - We prove the global existence of the smooth solutions near equilibrium to the Cauchy problem of the incompressible non-resistive magnetohydrodynamic equations in the whole three dimensional space. The result has been obtained by Xu and Zhang [SIAM J. Math. Anal. 47, 26-65 (2015)] and by Abidi and Zhang [Commun. Pure Appl. Math. 70, 1509-1561 (2017)] in anisotropic Besov space framework. In this paper, we provide a new proof based on the temporal weighted energy method.

UR - https://www.webofscience.com/wos/woscc/full-record/WOS:001520591200006

UR - https://www.scopus.com/pages/publications/105009768692

U2 - 10.1063/5.0267433

DO - 10.1063/5.0267433

M3 - Journal Article

AN - SCOPUS:105009768692

SN - 0022-2488

VL - 66

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

IS - 7

M1 - 071501

ER -

On the energy method for the global solutions to the three dimensional incompressible non-resistive MHD near equilibrium

Abstract

Bibliographical note

Access to Document

Other files and links

Fingerprint

Cite this