Linear theory of steady X-point magnetic reconnection

Slow magnetic reconnection at a neutral X-point of a two-dimensional magnetic field is studied in an incompressible viscous resistive fluid. It is shown analytically that the combined effect of viscosity and resistivity resolves the current singularity appearing in both the ideal and resistive magnetohydrodynamic approximations at the X-point and along the separatrices when the flow is allowed to cross them. A previous attempt had retained a weak singularity at third order. A two-parameter family of exact solutions describing the structure of the flow and current density distribution is found for the corresponding basic equations.