分数阶扩散的MHD-Boussinesq系统的全局正则性

Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (6): 1805-1815.

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Global Regularity for the MHD-Boussinesq System with Fractional Diffusion

Jing Yang¹(),Xuemei Deng^1,²(),Yanping Zhou^1,^2,*()

¹ College of Science, China Three Gorges University, Hubei Yichang 443002
² Three Gorges Mathematical Research Center, China Three Gorges University, Hubei Yichang 443002

Received:2021-03-12 Online:2021-12-26 Published:2021-12-02
Contact: Yanping Zhou E-mail:1972639378@qq.com;dxmeisx@126.com;zhyp5208@163.com
Supported by:
the NSFC(11901346);the NSFC(11871305);the Research Fund for Excellent Dissertation of China Three Gorges University(2021SSPY148)

Abstract

Abstract:

In this paper, we investigate the $n$-dimensional $(n\geq2)$ Magnetohydrodynamics-Boussinesq system with fractional diffusion. When the nonnegative constants $\alpha, \beta$ and $\gamma$ satisfy $\alpha\geq\frac{1}{2}+\frac{n}{4}, \ \alpha+\beta\geq 1+\frac{n}{2}$ and $\alpha+\gamma\geq\frac{n}{2}$, by using the energy methods, we obtain the global existence and uniqueness of solution for the system, which generalizes the existing result.

Key words: MHD-Boussinesq system, Global regularity, Fractional diffusion

CLC Number:

O175.2

Jing Yang,Xuemei Deng,Yanping Zhou. Global Regularity for the MHD-Boussinesq System with Fractional Diffusion[J].Acta mathematica scientia,Series A, 2021, 41(6): 1805-1815.

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References 20

1	Tran C V , Yu X W , Zhai Z C . On global regularity of 2D generalized magnetohydrodynamic equations. J Differ Equ, 2013, 254, 4194- 4216 doi: 10.1016/j.jde.2013.02.016
2	Jiu Q S , Zhao J F . A remark on global regularity of 2D generalized magnetohydrodynamic equations. J Math Anal Appl, 2014, 412, 478- 484 doi: 10.1016/j.jmaa.2013.10.074
3	Xu X J , Ye Z , Zhang Z J . Remark on an improved regularity criterion for the 3D MHD equations. Appl Math Lett, 2015, 42, 41- 46 doi: 10.1016/j.aml.2014.11.004
4	Wang Y Z , Wang K Y . Global well-posedness of the three dimensional magnetohydrodynamics equations. Nonlinear Anal RWA, 2014, 17, 245- 251 doi: 10.1016/j.nonrwa.2013.12.002
5	Wu J H . Generalized MHD equations. J Differ Equ, 2003, 195, 284- 312 doi: 10.1016/j.jde.2003.07.007
6	Hou T Y , Li C M . Global well-posedness of the viscous Boussinesq equations. Discrete Contin Dyn Syst, 2005, 12, 1- 12 doi: 10.3934/dcds.2005.12.1
7	Chae D . Global regularity for the 2D Boussinesq equations with partial viscosity terms. Adv Math, 2006, 203, 497- 513 doi: 10.1016/j.aim.2005.05.001
8	Ye Z . A note on global well-posedness of solutions to Boussinesq equations with fractional dissipation. Acta Math Sci, 2015, 35, 112- 120 doi: 10.1016/S0252-9602(14)60144-2
9	Yamazaki K , Pullman . On the global regularity of n-dimensional generalized Boussinesq system. Appl Math, 2015, 60, 109- 133 doi: 10.1007/s10492-015-0087-5
10	Bian D F , Gui G L . On 2-D Boussinesq equations for MHD convection with stratification effects. J Differ Equ, 2016, 261, 1669- 1711 doi: 10.1016/j.jde.2016.04.011
11	Bian D F , Liu J T . Initial-boundary value problem to 2D Boussinesq equations for MHD convection with stratification effects. J Differ Equ, 2017, 263, 8074- 8101 doi: 10.1016/j.jde.2017.08.034
12	Larios A , Pei Y . On the local well-posedness and a Prodi-Serrin-type regularity criterion of the three-dimensional MHD-Boussinesq system without thermal diffusion. J Differ Equ, 2017, 263, 1419- 1450 doi: 10.1016/j.jde.2017.03.024
13	Liu H M, Bian D F, Pu X K. Global well-posedness of the 3D Boussinesq-MHD system without heat diffusion. Z Angew Math Phys, 2019, 70, Article number: 81
14	别群益, 王其如, 姚正安. 修正的临界多孔介质方程Hölder连续解的正则性. 中国科学(数学), 2016, 46, 451- 466
	Bie Q Y , Wang Q R , Yao Z A . Regularity of Hölder continuous solutions of a modified critical porous media equation. Sci Sin Math, 2016, 46, 451- 466
15	李强. 分数阶扩散的三维液晶方程的整体正则性. 数学物理学报, 2020, 40A, 918- 924 doi: 10.3969/j.issn.1003-3998.2020.04.009
	Li Q . Global regularity for the 3D liquid crystal equations with fractional diffusion. Acta Math Sci, 2020, 40A, 918- 924 doi: 10.3969/j.issn.1003-3998.2020.04.009
16	Ye Z, Zhao X P. Global well-posedness of the generalized magnetohydrodynamic equations. Z Angew Math Phys, 2018, 69, Article number: 126
17	Chen Q L , Miao C X , Zhang Z F . On the regularity criterion of weak solution for the 3D viscous magneto-hydrodynamics equations. Commun Math Phys, 2008, 284, 919- 930 doi: 10.1007/s00220-008-0545-y
18	Wang W H , Qin T G , Bie Q Y . Global well-posedness and analyticity results to 3-D generalized magnetohydrodynamic equations. Appl Math Lett, 2016, 59, 65- 70 doi: 10.1016/j.aml.2016.03.009
19	Yamazaki K . Global regularity of logarithmically supercritical MHD system with zero diffusivity. Appl Math Lett, 2014, 29, 46- 51 doi: 10.1016/j.aml.2013.10.014
20	Wu J H . Global regularity for a class of generalized Magnetohydrodynamic equations. J Math Fluid Mech, 2011, 13, 295- 305 doi: 10.1007/s00021-009-0017-y

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Global Regularity for the MHD-Boussinesq System with Fractional Diffusion

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