Fan, Jishan; Liu, Dan; Zhou, Yong Uniform global strong solutions of the 2D magnetic Bénard problem in a bounded domain. (English) Zbl 1410.35114 Appl. Math. Lett. 86, 166-172 (2018). Summary: In this paper, we use the bootstrap argument to prove the uniform-in-\(k\) global strong solutions of the 2D magnetic Bénard problem in a bounded domain. Here \(k\) is the heat conductivity coefficient. Cited in 3 Documents MSC: 35Q35 PDEs in connection with fluid mechanics 76W05 Magnetohydrodynamics and electrohydrodynamics 76R10 Free convection 35D35 Strong solutions to PDEs 80A20 Heat and mass transfer, heat flow (MSC2010) Keywords:magnetic Bénard; heat conductivity; bounded domain PDFBibTeX XMLCite \textit{J. Fan} et al., Appl. Math. Lett. 86, 166--172 (2018; Zbl 1410.35114) Full Text: DOI References: [1] Galdi, G. P.; Padula, M., A new approach to energy theory in the stability of fluid motion, Arch. Ration. Mech. Anal., 110, 187-286 (1990) · Zbl 0719.76035 [2] Lai, M.; Pan, R.; Zhao, K., Initial boundary value problem for two-dimensional viscous Boussinesq equations, Arch. Ration. Mech. Anal., 199, 736-760 (2011) · Zbl 1231.35171 [3] Zhao, K., 2D inviscid heat conductive Boussinesq equations on a bounded domain, Michigan Math. J., 59, 2, 329-352 (2010) · Zbl 1205.35048 [4] Jin, L.; Fan, J.; Nakamura, G.; Zhou, Y., Partial vanishing viscosity limit for the 2D Boussinesq system with a slip boundary condition, Bound. Value Probl., 20 (2012) · Zbl 1282.35276 [5] Zhou, Y.; Fan, J.; Nakamura, G., Global Cauchy problem for a 2D magnetic Bénard problem with zero thermal conductivity, Appl. Math. Lett., 26, 6, 627-630 (2013) · Zbl 1355.35155 [6] Mulone, G.; Rionero, S., Necessary and sufficient conditions for nonlinear stability in the magnetic Bénard problem, Arch. Ration. Mech. Anal., 166, 197-281 (2003) · Zbl 1022.76020 [7] 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 [8] Yamazaki, K., Global regularity of generalized magnetic Bénard problem, Math. Methods Appl. Sci., 40, 2013-2033 (2017) · Zbl 1366.35147 [9] Ye, Z., Global regularity of the 2D magnetic Bénard system with partial dissipation, Adv. Differential Equations, 23, 193-238 (2018) · Zbl 1420.35267 [10] Tao, T., Nonlinear Dispersive Equations: Local and Global Analysis (2006), American Mathematical Society: American Mathematical Society Provindence, RI · Zbl 1106.35001 [11] Fan, J.; Li, F., Global strong solutions to the 3D full compressible Navier-Stokes system with vacuum in a bounded domain, Appl. Math. Lett., 78, 31-35 (2018) · Zbl 1384.35060 [12] Jiu, Q.; Niu, D.; Wu, J.; Xu, X.; Yu, H., The 2D magnetohydrodynamic equations with magnetic diffusion, Nonlinearity, 28, 3935-3955 (2015) · Zbl 1328.76076 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.