Magnetic collapse near zero points of the magnetic field

An analysis is presented of an exact set of solutions of the magnetohydrodynamic equations describing flows with homogeneous deformations in the vicinity of magnetic zero lines and having a singularity. The structure of the flow and of the magnetic field reveals a trend toward formation of strong quasi one-dimensional currents, pinch current sheets, in the spatially inhomogeneous case. The possibility of formation of current sheets in sheared flows in a cold and incompressible plasma is indicated.