I will present some (old) results on the transport and dissipation of enstrophy in 2D incompressible flows, after prior work by Gregory Eyink. I will
consider initial data with vorticity in $L^2$ and its logarithmic
refinements and study exact transport of enstrophy by the velocity
field. I will also consider data in the larger Besov space $B^{0}_{2,\infty}$
and study the existence of well-defined enstrophy defects, measuring the rate of enstrophy dissipation.
This is joint work with Milton Lopes and Helena Nussenzveig Lopes.
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