Stability of Two-Dimensional Incompressible MHD Equations with Mixed Partial Dissipation

This paper investigates the stabilization effect of the two-dimensional incompressible MHD system with partial dissipation near a background magnetic field. Employing time-global uniform a priori estimates, we establish the global well-posedness of the nonlinear MHD equations in𝐻3(ℝ2). Building upon this fundamental result, we derive the large-time asymptotic behavior of the solutions.