Matsuoka et al.  present a set of equations governing the evolution of two-dimensional MHD flows using current-vortex sheets. In the resulting model the vorticity ω and current density j are zero except on the current-vortex sheets. We show that this is not true in general and that the term Δ(B × u) in the evolution equation for j does not vanish, leading to the generation of j and ω in the bulk. This means that the evolution of the system is not governed solely by the dynamics of quantities on the current-vortex sheets. A perturbative solution is derived that shows this explicitly.
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