Global solutions demonstrate stability in three-dimensional incompressible magnetohydrodynamics, indicating important properties of fluid behavior.
This paper concerns the Cauchy problem of three-dimensional (3D) axisymmetric inhomogeneous incompressible magnetohydrodynamics (MHD) system with initial data (ρ0,u0,b0)=(ρ0,u0rer+u0θeθ+u0zez,b0θeθ). It is established that this system is globally well-posed if the initial data ‖1r(1ρ0−1)‖L∞ and ‖u0θ‖L3 are sufficiently small. Moreover, we obtain the decay estimate of the angular velocity uθ.
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Liu et al. (2026) studied this question.
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