Abstract

Magnetic reconnection is known in plasma physics as a singularity formation on the current density, or on the lines of the magnetic field. Physicists except that 3D incompressible Hall MHD is a good model for the fast magnetic reconnection. We will present a new result that we obtained on 3D incompressible viscous Hall MHD without resistivity. We prove that the singularity is of self-similar nature and is stable in the analytic topology. This is the first result of smooth blowup on 3D incompressible Navier stokes even if the blow up mechanism is due to the Hall effect on the magnetic field.

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