The analysis is applied to investigate stability to low perturbation of the flow of electrically conducting viscous incompressible fluid between two coaxial unbounded cylinders affected by a longitudinal magnetic field. We use a complete system of magnetohydrodynamic equations and effective method of differential run to study in detail the influence of the critical Reynolds number on electric conductivity. The jump stabilization has been observed.

Key worlds: hydrodynamics stability, magnetohydrodynamics.