Stability and large time decay for the 3D anisotropic MHD-Boussinesq equations near the hydrostatic equilibrium
Source abstract
Abstract
This paper investigates the three-dimensional anisotropic magnetohydrodynamics-Boussinesq equations with horizontal fractional dissipation for perturbations around the hydrostatic equilibrium. By thoroughly leveraging the system’s inherent structure, energy-based approaches, and bootstrapping argument techniques, we demonstrate the global stability of the system and the decay rates induced by sufficiently small initial data.
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Research context
OpenAlex topics: Navier-Stokes equation solutions · Stability and Controllability of Differential Equations · Advanced Mathematical Physics Problems
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Affiliations
School of Mathematical Sciences, Shenzhen University , Shenzhen 518060,
References (27)
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1. Théorie des ondes et des remous qui se propagent le long d'un canal rectangulaire horizontal, en communiquant au liquide contenu dans ce canal des vitesses sensiblement pareilles de la surface au fond
2. Global regularity and time decay for the 2D magnetohydrodynamic equations with fractional dissipation and partial magnetic diffusion10.1007/s00021-018-0376-3 ↗
3. 1987
4. 1989
5. Kinetic derivation of fractional Stokes and Stokes-Fourier systems10.3934/krm.2016.9.105 ↗
6. Initial boundary value problem for two-dimensional viscous Boussinesq equations for MHD convection10.3934/dcdss.2016065 ↗
7. On 2-D Boussinesq equations for MHD convection with stratification effects10.1016/j.jde.2016.04.011 ↗
8. Initial-boundary value problem to 2D Boussinesq equations for MHD convection with stratification effects10.1016/j.jde.2017.08.034 ↗
9. Global smooth axisymmetic solutions of the Boussinesq equations for magnetohydrodynamics convection10.1007/s00021-019-0468-8 ↗
10. Global well-posedness of the 3D Boussinesq-MHD system without heat diffusion10.1007/s00033-019-1126-y ↗
11. On the local well-posedness and a Prodi–Serrin-type regularity criterion of the three-dimensional MHD-Boussinesq system without thermal diffusion10.1016/j.jde.2017.03.024 ↗
12. Global existence and decay estimates of solutions to the MHD–Boussinesq system with stratification effects10.1088/1361-6544/ac93e0 ↗
13. Global regularity of 2D temperature-dependent MHD-Boussinesq equations with zero thermal diffusivity10.1016/j.jde.2021.05.040 ↗
14. Global well-posedness for the 2D MHD-Boussinesq system with temperature-dependent diffusion10.1016/j.aml.2020.106399 ↗
15. Global well-posedness for the MHD-Boussinesq system with the temperature-dependent viscosity10.1016/j.nonrwa.2018.05.006 ↗
16. Stability of Couette flow for 2D Boussinesq system in a uniform magnetic field with vertical dissipation10.1016/j.aml.2021.107415 ↗
17. Stability of hydrostatic equilibrium for the 2D BMHD system with partial dissipation10.3934/cpaa.2022109 ↗
18. Stability of Couette flow for 2D Boussinesq system with vertical dissipation10.1016/j.jfa.2021.109255 ↗
19. Stability and exponential decay for the 2D anisotropic Boussinesq equations with horizontal dissipation10.1007/s00526-021-01976-w ↗
20. The resistive magnetohydrodynamic equation near an equilibrium10.1016/j.jde.2019.09.027 ↗
21. Influence of a background magnetic field on a 2D magnetohydrodynamic flow10.1088/1361-6544/abb928 ↗
22. Time decay and stability of solutions for the 3D density-dependent incompressible Boussinesq system10.3934/dcdsb.2022188 ↗
23. Stabilization of a background magnetic field on a 2 dimensional magnetohydrodynamic flow10.1137/20m1324776 ↗
24. Decay for the 3D anisotropic MHD-Boussinesq equations near the hydrostatic equilibrium10.1007/s00033-023-02011-y ↗
25. Stability and sharp decay for 3D incompressible MHD system with fractional horizontal dissipation and magnetic diffusion10.1007/s00033-023-01939-5 ↗
26. 2006
27. 2002