Asymptotic stability and decay rates for the 2D magnetic Bénard fluid equations with mixed partial dissipation, magnetic diffusion and thermal diffusivity. (English) Zbl 1508.35175
Summary: We consider the asymptotic stability and large-time behavior for the 2D magnetic Bénard fluid equations with mixed partial dissipation, magnetic diffusion and thermal diffusivity. More precisely, we acquire the asymptotic stability and decay rate for the system on two perturbations near two steady state solutions \((\tilde{u},\tilde{b},\tilde{\theta},\tilde{p})\) and \((\check{u},\check{b},\check{\theta},\check{p})\), respectively.
MSC:
| 35Q60 | PDEs in connection with optics and electromagnetic theory |
| 35Q35 | PDEs in connection with fluid mechanics |
| 76W05 | Magnetohydrodynamics and electrohydrodynamics |
References:
| [1] | Cheng, J.; Du, L., On two-dimensional magnetic Bénard problem with mixed partial viscosity, J. Math. Fluid Mech., 17, 769-797 (2015) · Zbl 1329.35245 |
| [2] | Doering, C. R.; Wu, J.; Zhao, K.; Zheng, X., Long time behavior of the two-dimensional Boussinesq equations without buoyancy diffusion, Physica D, 376, 144-159 (2018) · Zbl 1398.35164 |
| [3] | Ji, R.; Li, D.; Wei, Y.; Wu, J., Stability of hydrostatic equilibrium to the 2D Boussinesq systems with partial dissipation, Appl. Math. Lett., 98, 392-3974 (2019) · Zbl 1448.35397 |
| [4] | Ji, R.; Lin, H.; Wu, J.; Yan, L., Stability for a system of the 2D magnetohydrodynamic equations with partial dissipation, Appl. Math. Lett., 94, 244-249 (2019) · Zbl 1417.35126 |
| [5] | Lin, F.; Xu, L.; Zhang, P., Global small solutions of 2-D incompressible MHD system, J. Differ. Equ., 259, 10, 5440-5485 (2015) · Zbl 1321.35138 |
| [6] | Ma, L., Global existence of smooth solutions for three-dimensional magnetic Bénard system with mixed partial dissipation, magnetic diffusion and thermal diffusivity, J. Math. Anal. Appl., 461, 2, 1639-1652 (2018) · Zbl 1390.35277 |
| [7] | Ma, L., Global regularity for the 2D magnetic Bénard fluid system with mixed partial viscosity, Comput. Math. Appl., 76, 9, 2148-2166 (2018) · Zbl 1442.76147 |
| [8] | Ma, L., Global regularity results for the \(2 \frac{1}{2}\) D magnetic Bénard system with mixed partial viscosity, Appl. Anal., 98, 6, 1143-1164 (2019) · Zbl 1414.35172 |
| [9] | Ma, L.; Ji, R., Blow-up criteria for \(2 \frac{1}{2}\) D magnetic Bénard fluid system with partial viscosity, Appl. Math. Comput., 346, 816-831 (2019) · Zbl 1428.35384 |
| [10] | Ren, X.; Wu, J.; Xiang, Z.; Zhang, Z., Global existence and decay of smooth solution for the 2-D MHD equations without magnetic diffusion, J. Funct. Anal., 267, 2, 503-541 (2014) · Zbl 1295.35104 |
| [11] | Tao, K.; Wu, J.; Zhao, K.; Zheng, X., Stability near hydrostatic equilibrium to the 2D Boussinesq equations without thermal diffusion, Arch. Ration. Mech. Anal. (2019) |
| [12] | Wu, J.; Wu, Y.; Xu, X., Global small solution to the 2D MHD system with a velocity damping term, SIAM J. Math. Anal., 47, 4, 2630-2656 (2015) · Zbl 1366.35145 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
