In this paper, we investigate an initial boundary value problem of a planar magnetohydrodynamics system with temperature-dependent viscosity, heat conductivity, and resistivity. When all of the relative coefficients mentioned above are power functions of temperature, the existence and uniqueness of a global-in-time non-vacuum strong solutions are proved under some special assumptions. At the same time, we obtain the nonlinear exponential stability of the solution. In fact, the initial data could be large if the power of viscosity is small enough.
Citation: Dandan Song, Xiaokui Zhao. Large time behavior of strong solution to the magnetohydrodynamics system with temperature-dependent viscosity, heat-conductivity, and resistivity[J]. Electronic Research Archive, 2025, 33(2): 938-972. doi: 10.3934/era.2025043
In this paper, we investigate an initial boundary value problem of a planar magnetohydrodynamics system with temperature-dependent viscosity, heat conductivity, and resistivity. When all of the relative coefficients mentioned above are power functions of temperature, the existence and uniqueness of a global-in-time non-vacuum strong solutions are proved under some special assumptions. At the same time, we obtain the nonlinear exponential stability of the solution. In fact, the initial data could be large if the power of viscosity is small enough.
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Dandan Song, Xiaokui Zhao. Large time behavior of strong solution to the magnetohydrodynamics system with temperature-dependent viscosity, heat-conductivity, and resistivity[J]. Electronic Research Archive, 2025, 33(2): 938-972. doi: 10.3934/era.2025043
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