具有分数阶耗散的三维温度相关不可压缩 MHD-Boussinesq 方程的全局强解

具有分数阶耗散的三维温度相关不可压缩 MHD-Boussinesq 方程的全局强解

Global Strong Solution of 3D Temperature-Dependent Incompressible MHD-Boussinesq Equations with Fractional Dissipation

摘要/Abstract

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数学物理学报 ›› 2025, Vol. 45 ›› Issue (2): 418-433.

刘辉¹,林琳²,孙成峰^3,^*()

¹济南大学数学科学学院济南 250022
²上海电机学院文理学院上海 201306
³南京财经大学应用数学学院南京 210023

收稿日期:2023-10-24 修回日期:2024-09-25 出版日期:2025-04-26 发布日期:2025-04-09
通讯作者: 孙成峰 E-mail:sch200130@163.com
基金资助:
国家自然科学基金(12271293);国家自然科学基金(11901342);国家自然科学基金(12371445);国家自然科学基金(11901302);国家自然科学基金(11701269);山东省高校青年创新团队项目(2023KJ204);山东省自然科学基金(ZR2023MA002);江苏省自然科学基金(BK20231301)

Hui Liu¹,Lin Lin²,Chengfeng Sun^3,^*()

¹School of Mathematical Sciences, University of Jinan, Jinan 250022
²School of Arts and Sciences, Shanghai Dianji University, Shanghai 201306
³School of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210023

Received:2023-10-24 Revised:2024-09-25 Online:2025-04-26 Published:2025-04-09
Contact: Chengfeng Sun E-mail:sch200130@163.com
Supported by:
NSFC(12271293);NSFC(11901342);NSFC(12371445);NSFC(11901302);NSFC(11701269);Project of Youth Innovation Team of Universities of Shandong Province(2023KJ204);Natural Science Foundation of Shandong Province(ZR2023MA002);Natural Science Foundation of Jiangsu Province(BK20231301)

摘要：

该文研究了具有与温度相关的热扩散率和电阻率的三维广义不可压缩 MHD-Boussinesq 方程. 在 Sobolev 空间 $H^{s}$ 中, 对于任意 $s>2$ , 证明了具有温度相关热扩散率和电阻率的三维广义不可压缩 MHD-Boussinesq 方程存在唯一的全局强解.

关键词: MHD-Boussinesq方程, 强解, 热扩散率

Abstract:

The 3D generalized incompressible MHD-Boussinesq equations with temperature-dependent thermal diffusivity and electrical resistivity are considered in this paper. We prove that there is a unique global strong solution of the 3D generalized incompressible MHD-Boussinesq equations with temperature-dependent thermal diffusivity and electrical resistivity in the Sobolev spaces $H^{s}$ for any $s>2$ .

Key words: MHD-Boussinesq equations, strong solution, thermal diffusivity

中图分类号:

O175.2

刘辉,林琳,孙成峰. 具有分数阶耗散的三维温度相关不可压缩 MHD-Boussinesq 方程的全局强解[J]. 数学物理学报, 2025, 45(2): 418-433.

Hui Liu,Lin Lin,Chengfeng Sun. Global Strong Solution of 3D Temperature-Dependent Incompressible MHD-Boussinesq Equations with Fractional Dissipation[J]. Acta mathematica scientia,Series A, 2025, 45(2): 418-433.

[1]	Abidi H, Zhang P. On the global well-posedness of 2-D Boussinesq system with variable viscosity. Adv Math, 2016, 305: 1202-1249
[2]	Abidi H, Zhang P. On the global well-posedness of 3-D Boussinesq system with variable viscosity. Chin Ann Math Ser B, 2019, 40(5): 643-688
[3]	Amann H. Linear and Quasilinear Parabolic Problems. Boston: Birkhäuser Boston Inc, 1995
[4]	Bahouri H, Chemin J Y, Danchin R. Fourier Analysis and Nonlinear Partial Differential Equations. Heidelberg: Springer, 2011
[5]	Bian D F. Initial boundary value problem for two-dimensional viscous Boussinesq equations for MHD convection. Discrete Contin Dyn Syst Ser S, 2016, 9(6): 1591-1611
[6]	Bian D F, Gui G L. On 2-D Boussinesq equations for MHD convection with stratification effects. J Differ Equ, 2016, 261(3): 1669-1711
[7]	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(12): 8074-8101
[8]	Chen C, Liu J T. Global well-posedness of 2D nonlinear Boussinesq equations with mixed partial viscosity and thermal diffusivity. Math Methods Appl Sci, 2017, 40(12): 4412-4424
[9]	Chen Q L, Jiang L Y. Global well-posedness for the 2-D Boussinesq system with temperature-dependent thermal diffusivity. Colloq Math, 2014, 135(2): 187-199
[10]	Dong B Q, Li C Y, Xu X J, Ye Z. Global smooth solution of 2D temperature-dependent tropical climate model. Nonlinearity, 2021, 34(8): 5662-5686
[11]	Fan J S, Li F C, Nakamura G. Regularity criteria and uniform estimates for the Boussinesq system with temperature-dependent viscosity and thermal diffusivity. J Math Phys, 2014, 55(5): Article 051505
[12]	Fan J S, Li F C, Nakamura G. Regularity criteria for the Boussinesq system with temperature-dependent viscosity and thermal diffusivity in a bounded domain. Discrete Contin Dyn Syst, 2016, 36(9): 4915-4923
[13]	Ghani M. Local well-posedness of Boussinesq equations for MHD convection with fractional thermal diffusion in Sobolev space $H^{s}(\mathbb{R}^{n})\times H^{s+1-\epsilon}(\mathbb{R}^{n})\times H^{s+\alpha-\epsilon}(\mathbb{R}^{n})$ . Nonlinear Anal: Real World Appl, 2021, 62: 103355
[14]	Jiu Q S, Liu J T. Global-wellposedness of 2D Boussinesq equations with mixed partial temperature-dependent viscosity and thermal diffusivity. Nonlinear Anal, 2016, 132: 227-239
[15]	Jiang K R, Liu Z H, Zhou L. Global existence and asymptotic stability of 3D generalized magnetohydrodynamic equations. J Math Fluid Mech, 2020, 22(1): Article 9
[16]	Kato T, Ponce G. Commutator estimates and the Euler and Navier-Stokes equations. Comm Pure Appl Math, 1988, 41(7): 891-907
[17]	Kenig C E, Ponce G, Vega L. Well-posedness and scattering results for the generalized Korteweg-de Vries equation via the contraction principle. Comm Pure Appl Math, 1933, 46(4): 527-620
[18]	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(2): 1419-1450
[19]	Li C Y, Xu X J, Ye Z. On long-time asymptotic behavior for solutions to 2D temperature-dependent tropical climate model. Discrete Contin Dyn Syst, 2022, 42(3): 1535-1568
[20]	Li H P, Pan R H, Zhang W Z. Initial boundary value problem for 2D Boussinesq equations with temperature-dependent diffusion. J Hyperbolic Differ Equ, 2015, 12: 469-488
[21]	Liu H, Deng H Y, Lin L, Sun C F. Well-posedness of the 3D Boussinesq-MHD equations with partial viscosity and damping. J Math Anal Appl, 2022, 515(2): Article 126437
[22]	Liu H, Lin L, Sun C F. Well-posedness of the generalized Navier-Stokes equations with damping. Appl Math Lett, 2021, 121: Article 107471
[23]	Liu H, Sun C F, Xin J. Well-posedness for the hyperviscous magneto-micropolar equations. Appl Math Lett, 2020, 107: Article 106403
[24]	Liu H, Sun C F, Xin J. Attractors of the 3D magnetohydrodynamics equations with damping. Bull Malays Math Sci Soc, 2021, 44(1): 337-351
[25]	Sun Y Z, Zhang Z F. Global regularity for the initial-boundary value problem of the 2-D Boussinesq system with variable viscosity and thermal diffusivity. J Differ Equ, 2013, 255(6): 1069-1085
[26]	Tran C V, Yu X W, Zhai Z C. On global regularity of 2D generalized magnetohydrodynamic equations. J Differ Equ, 2013, 254(10): 4194-4216
[27]	Wang C, Zhang Z F. Global well-posedness for the 2-D Boussinesq system with the temperature-dependent viscosity and thermal diffusivity. Adv Math, 2011, 228(1): 43-62
[28]	Wang S S, Xu W Q, Liu J T. Global well-posedness and large time behavior to 2D Boussinesq equations for MHD convection. Methods Appl Anal, 2022, 29(1): 31-56
[29]	Wu J H. Generalized MHD equations. J Differ Equ, 2003, 195(2): 284-312
[30]	Wu J H. Regularity criteria for the generalized MHD equations. Comm Partial Differential Equations. 2008, 33(2): 285-306
[31]	Wu J H. Global regularity for a class of generalized magnetohydrodynamic equations. J Math Fluid Mech. 2011, 13(2): 295-305
[32]	Ye Z. Global regularity of 2D temperature-dependent MHD-Boussinesq equations with zero thermal diffusivity. J Differ Equ, 2021, 293: 447-481
[33]	Ye Z. Global well-posedness for a model of 2D temperature-dependent Boussinesq equations without diffusivity. J Differ Equ, 2021, 271: 107-127
[34]	Zhou Y. Regularity criteria for the generalized viscous MHD equations. Ann Inst H Poincaré C Anal Non Linéaire, 2007, 24(3): 491-505

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