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Uniform global strong solutions of the 2D magnetic Bénard problem in a bounded domain. (English) Zbl 1410.35114

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.

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)
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[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
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