速度零耗散且温度分数阶扩散的二维微极Rayleigh-Bénard对流系统的全局正则性

Abstract

Abstract:

This paper studies the global regularity problem for the 2D micropolar Rayleigh-Bénard convection system with velocity zero dissipation, micro-rotation velocity Laplace dissipation and temperature fractional dissipation. By introducing two combined quantities and using the technique of Littlewood-Paley decomposition, this paper establishes the global regularity result of solutions to this system.

Key words: Micropolar Rayleigh-Bénard, Global regularity, Besov space, Sobolev space

CLC Number:

O175.29

Li Changhao, Yuan Baoquan. Global Regularity for the 2D Micropolar Rayleigh-Bénard Convection System with Velocity Zero Dissipation and Temperature Fractional Diffusion[J].Acta mathematica scientia,Series A, 2024, 44(4): 914-924.

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References 28

[1]	Bahouri H, Chemin J Y, Danchin R. Fourier Analysis and Nonliear Partial Differential Equations. Berlin: Springer-Verlag, 2011
[2]	Chae D H. Global regularity for the 2D Boussinesq equations with partial viscosity terms. Adv Math, 2006, 203(2): 497-513
[3]	Chen M T. Global well-posedness of the 2D incompressible micropolar fluid flows with partial viscosity and angular viscisiy. Acta Math Sci, 2013, 33B(4): 929-935
[4]	Chen Q L, Miao C X, Zhang Z F. A new Bernstein inequality and the 2D dissipative quasigeostrophic equation. Comm Math Phys, 2007, 271: 821-838
[5]	Deng L H, Shang H F. Global regularity for the micropolar Rayleigh-Bénard problem with only velocity dissipation. Proc Roy Soc Edinburgh Sect, 2022, 152A(5): 1109-1138
[6]	Dong B Q, Li J N, Wu J H. Global well-posedness and large-time decay for the 2D micropolar equations. J Differential Equations, 2017, 262: 3488-3523
[7]	Dong B Q, Zhang Z F. Global regularity of the 2D micropolar fluid flows with zero angular viscosity. J Differential Equations, 2010, 349(1): 200-213
[8]	Dong Y, Huang Y F, Li L, Lu Q. The regularity criteria of weak solutions to 3D axisymmetric incompressible Boussinesq equations. Acta Math Sci, 2023, 43(6): 2387-2397
[9]	Eringen A C. Theory of micropolar fluids. J Math Mech, 1966, 16: 1-18
[10]	Galdi G P, Rionero S. A note on the existence and uniqueness of solutions of micropolar fluid equations. Internet J Engrg Sci, 1977, 15(2): 105-108
[11]	Hanachi A, Houamed H, Zerguine M. On the global well-posedness of the axisymmetric viscous Boussinesq system in critical Lebesgue spaces. Discrete Contin Dyn Syst, 2020, 40(11): 6473-6506
[12]	Hmidi T, Keraani S. On the global well-posedness of the two-dimensional Boussinesq system with a zero diffusivity. Adv Differential Equations, 2007, 12(4): 461-480
[13]	Hmidi T, Keraani S, Rousset F. Global well-posedness for a Boussinesq-Navier-Stokes system with critical dissipation. J Differential Equations, 2010, 249: 2147-2174
[14]	Jin X T, Xiao Y L, Y H. Global well-posedness of the 2D Boussinesq equations with partial dissipation. Acta Math Sci, 2022, 42B(4): 1293-1309
[15]	Kalita P, Łukaszewicz G. Micropolar meets Newtonian in 3D. The Rayleigh-Bénard problem for large Prandtl numbers. Nonlinearity, 2020, 33: 5686-5732
[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 of the initial value problem for the Korteweg-de Vries equations. J Amer Math Soc, 1991, 4(2): 323-347
[18]	Kalita P, Lange J, Łukaszewicz G. Micropolar meets Newtonian. The Rayleigh-Bénard problem. Physical D, 2019, 392: 57-80
[19]	苗长兴. 调和分析及其在偏微分方程中的应用(第二版). 北京: 科学出版社, 2004
	Miao C X. Harmonic Analysis and Application to Partial Differential Equations(Second Edition). Beijing: Science Press, 2004
[20]	Ning J. The maximum principle and the global attractor for the dissipative 2D quasi-geostrophic equations. Comm Math Phys, 2005, 255(1): 161-181
[21]	Schonbek M E, Schonbek T. Moments and lower bounds in the far-field of solutions to quasi-geostrophic flows. Discrete Contin Dyn Syst, 2005, 13: 1277-1304
[22]	Tarasińska A. Global attractor for heat convection problem in a micropolar fluid. Math Methods Appl Sci, 2005, 29: 1215-1236
[23]	Triebel H. Theory of Function Spaces. Basel: Birkhäuser Verlag, 1983
[24]	Wang S. Global well-posedness for the 2D micropolar Rayleigh-Bénard convection problem without velocity dissipation. Acta Math Sin, 2021, 37(7): 1053-1065
[25]	Wu G, Xue L T. Global well-posedness for the 2D Bénard system with fractional diffusivity and Yudovich's type data. J Differential Equations, 2012, 253: 100-125
[26]	Xu F Y, Chi M L. Global regularity for the 2D micropolar Rayleigh-Bénard convection system with the zero diffusivity. Appl Math Lett, 2020, 108: 106508
[27]	Ye Z. Some new regularity criteria for the 2D Euler-Boussinesq equations via the temperature. Acta Appl Math, 2018, 157: 141-169
[28]	Yuan B Q. On the regularity criteria of weak solutions to the micropolar fluid equations in Lorentz space. Proc Amer Math Soc, 2010, 138: 2025-2036

Global Regularity for the 2D Micropolar Rayleigh-Bénard Convection System with Velocity Zero Dissipation and Temperature Fractional Diffusion

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