Acta mathematica scientia,Series A ›› 2023, Vol. 43 ›› Issue (3): 754-770.
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Received:
2022-06-29
Revised:
2023-02-06
Online:
2023-06-26
Published:
2023-06-01
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CLC Number:
Li Xiaoli,Chen Xiaoli. Stability and Exponential Decay of the 3D Boussinesq Equations with Partial Dissipation[J].Acta mathematica scientia,Series A, 2023, 43(3): 754-770.
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[1] | Said O B, Pandey U R, Wu J. The stabilizing effect of the temperature on buoyancy driven fluids. arXiv Preprint. arXiv:2005.11661, 2020 |
[2] | Cao C, Wu J. Global regularity for the 2D MHD equations with mixed partial dissipation and magnetic diffusion Adv. Math, 2011, 226: 1803-1822 |
[3] | Castro A, Cordoba D, Lear D. On the asymptotic stability of stratified solutions for the 2D Boussinesq equations with a velocity damping term. Math Models Appl Sci, 2019, 29: 1227-1277 |
[4] |
Deng W, Wu J, Zhang P. Stability of Couette flow for 2D Boussinesq system with vertical dissipation. J Functional Analysis, 2021, 281(12): 109255
doi: 10.1016/j.jfa.2021.109255 |
[5] |
Doering C R, Wu J, Zhao K, Zheng X. Long time behavior of the two-dimensional Boussinesq equations without buoyancy diffusion. Physics D, 2018, 376/377: 144-159
doi: 10.1016/j.physd.2017.12.013 |
[6] |
Dong B Q, Wu J, Xu X, Zhu N. Stability and exponential decay for the 2D anisotropic Boussinesq equations with horizontal dissipation. Calculus of Variations and Partial Differential Equations, 2021, 60: 116
doi: 10.1007/s00526-021-01976-w |
[7] |
Lai S, Wu J, Zhong Y. Stability and large-time behavior of the 2D Boussinesq equations with partial dissipation. Journal of Differential Equations, 2021, 271: 764-796
doi: 10.1016/j.jde.2020.09.022 |
[8] | Majda A J. Introduction to PDEs and Waves for the Atmosphere and Ocean. Courant Lecture Notes on Mathematics, Vol 9. Providence: Americon Mathematical Soc, 2003 |
[9] | Majda A J, Bertozzi A L. Vorticity and Incompressible Flow. Cambridge: Cambridge University Press, 2002 |
[10] |
Tao L, Wu J. The 2D Boussinesq equations with vertical dissipation and linear stability of shear flows. J Differential Equations, 2019, 267: 1731-1747
doi: 10.1016/j.jde.2019.02.020 |
[11] |
Tao L, Wu J, Zhao K, Zheng X. Stability near hydrostatic equilibrium to the 2D Boussinesq equations without thermal diffusion. Arch Ration Mech Anal, 2020, 237: 585-630
doi: 10.1007/s00205-020-01515-5 |
[12] |
Wu J, Zhang Q. Stability and optimal decay for a system of 3D anisotropic Boussinesq equations. Nonlinearity, 2021, 34: 5456
doi: 10.1088/1361-6544/ac08e9 |
[13] |
Zillenger C. On enhanced dissipation for the Boussinesq equations. J Differential Equations, 2021, 282: 407-445
doi: 10.1016/j.jde.2021.02.029 |
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