Solutions of the hydromagnetic equation with magnetic null points

Numerical simulations of magnetic reconnection with uniform resistivity show that the length of the current sheet increases for increasing magnetic Reynolds number. In order to prevent the current sheet from growing in general the resistivity is assumed to be localized. For uniform resistivity the reconnection proceeds much slower than for localized resistivity. In this paper analytical solutions of the hydromagnetic equation are presented for localized and uniform resistivity. It is shown that there exists an essential singularity in the behaviour of a solution of magnetic reconnection in the limit of large magnetic Reynolds number: For prescribed boundary conditions the solution for localized resistivity does not approach the solution for uniform resistivity in the limit of large magnetic Reynolds number.