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We construct examples of smooth periodic solutions to the Magnetohydrodynamicequations in dimension 2 with positive resistivity for which the topology ofthe magnetic lines changes under the flow. By Alfv\'en's theorem this is knownto be impossible in the ideal case (resistivity = 0). In the resistive case thereconnection of the magnetic lines is known to occur and has deep physicalimplications, being responsible for many dynamic phenomena in astrophysics. Theconstruction is a simplified proof of [3] and in addition we consider the caseof the forced system.

On the topology of the magnetic lines of solutions of the MHD equations