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

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

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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.

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[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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