In this paper, the linear stability analysis for ideal incompressible magnetohydrodynamic (MHD) flows is investigated. MHD flows in cylindrical domains with arbitrary cross-section as well as circular cross-section are considered. A solution method for obtaining solutions of the full MHD equations of incompressible flow is constructed. Two criteria around the linear stability of that flow are applied to several nonlinear equilibria with constant and non-constant Mach number. The constructed method is exploited in obtaining sufficient conditions for linear stability of the former equilibria.
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