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

38 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

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10.1007/s00033-019-1126-y

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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",

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AU - Pu, Xueke

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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

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DO - 10.1007/s00033-019-1126-y

M3 - Article

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ER -

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

Abstract

Keywords

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