DOI: 10.1063/5.0316990 ISSN: 0022-2488
Global well-posedness of the magnetohydrodynamic system with mixed dissipation around a constant magnetic field background
Xia Chen, Jinkai Li, Liening QiaoIn this paper, we study the global well-posedness and decaying rate of the three dimensional magnetohydrodynamic equations, either with horizontal viscosity and vertical magnetic diffusion or with vertical viscosity and horizontal magnetic diffusion around any constant magnetic field background ω=(ω1,ω2,ω3)∈R3 with ω3 ≠ 0 and (ω1, ω2) satisfying the Diophantine condition.