On a model for the Navier-Stokes equations using magnetization variables

Our main focus is the proof of global well-posedness in H1/2 for a new variant of (1), where Pw is replaced by w in the second nonlinear term:(2)∂tw+(Pw⋅∇)w+12∇|w|2−Δw=0. This is based on a maximum principle, analogous to a similar property of the Burgers equations.