Global well-posedness of the 3D Boussinesq-MHD system without heat diffusion

Huimin Liu; Dongfen Bian; Xueke Pu

doi:10.1007/s00033-019-1126-y

Global well-posedness of the 3D Boussinesq-MHD system without heat diffusion

Huimin Liu, Dongfen Bian^*, Xueke Pu

^*Corresponding author for this work

School of Mathematics and Statistics

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

33 Citations (Scopus)

Abstract

In this paper, we show the global existence and uniqueness of strong and smooth large solutions to the 3D Boussinesq-MHD system without heat diffusion. Since the temperature satisfies a transport equation, in order to get high regularity of temperature, we need to use the combination of estimates about velocity and magnetic field. Moreover, our system involves a nonlinear damping term in the momentum equations due to the Brinkman–Forchheimer–extended-Darcy law of flow in porous media.

Original language	English
Article number	81
Journal	Zeitschrift fur Angewandte Mathematik und Physik
Volume	70
Issue number	3
DOIs	https://doi.org/10.1007/s00033-019-1126-y
Publication status	Published - 1 Jun 2019

Keywords

3D Boussinesq-MHD system
Global well-posedness
Strong and smooth solution

Access to Document

10.1007/s00033-019-1126-y

Cite this

Liu, H., Bian, D., & Pu, X. (2019). Global well-posedness of the 3D Boussinesq-MHD system without heat diffusion. Zeitschrift fur Angewandte Mathematik und Physik, 70(3), Article 81. https://doi.org/10.1007/s00033-019-1126-y

@article{454581f4ead943dfb23ddb085d0f6930,

title = "Global well-posedness of the 3D Boussinesq-MHD system without heat diffusion",

abstract = "In this paper, we show the global existence and uniqueness of strong and smooth large solutions to the 3D Boussinesq-MHD system without heat diffusion. Since the temperature satisfies a transport equation, in order to get high regularity of temperature, we need to use the combination of estimates about velocity and magnetic field. Moreover, our system involves a nonlinear damping term in the momentum equations due to the Brinkman–Forchheimer–extended-Darcy law of flow in porous media.",

keywords = "3D Boussinesq-MHD system, Global well-posedness, Strong and smooth solution",

author = "Huimin Liu and Dongfen Bian and Xueke Pu",

note = "Publisher Copyright: {\textcopyright} 2019, Springer Nature Switzerland AG.",

year = "2019",

month = jun,

day = "1",

doi = "10.1007/s00033-019-1126-y",

language = "English",

volume = "70",

journal = "Zeitschrift fur Angewandte Mathematik und Physik",

issn = "0044-2275",

publisher = "Birkhauser Verlag Basel",

number = "3",

}

TY - JOUR

T1 - Global well-posedness of the 3D Boussinesq-MHD system without heat diffusion

AU - Liu, Huimin

AU - Bian, Dongfen

AU - Pu, Xueke

PY - 2019/6/1

Y1 - 2019/6/1

N2 - In this paper, we show the global existence and uniqueness of strong and smooth large solutions to the 3D Boussinesq-MHD system without heat diffusion. Since the temperature satisfies a transport equation, in order to get high regularity of temperature, we need to use the combination of estimates about velocity and magnetic field. Moreover, our system involves a nonlinear damping term in the momentum equations due to the Brinkman–Forchheimer–extended-Darcy law of flow in porous media.

AB - In this paper, we show the global existence and uniqueness of strong and smooth large solutions to the 3D Boussinesq-MHD system without heat diffusion. Since the temperature satisfies a transport equation, in order to get high regularity of temperature, we need to use the combination of estimates about velocity and magnetic field. Moreover, our system involves a nonlinear damping term in the momentum equations due to the Brinkman–Forchheimer–extended-Darcy law of flow in porous media.

KW - 3D Boussinesq-MHD system

KW - Global well-posedness

KW - Strong and smooth solution

UR - http://www.scopus.com/inward/record.url?scp=85065288177&partnerID=8YFLogxK

U2 - 10.1007/s00033-019-1126-y

DO - 10.1007/s00033-019-1126-y

M3 - Article

AN - SCOPUS:85065288177

SN - 0044-2275

VL - 70

JO - Zeitschrift fur Angewandte Mathematik und Physik

JF - Zeitschrift fur Angewandte Mathematik und Physik

IS - 3

M1 - 81

ER -

Global well-posedness of the 3D Boussinesq-MHD system without heat diffusion

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this