Seminar Analysis: Anna Mazzucato (Penn State University)

Enstrophy dissipation in 2D incompressible fluids

I will present some (old) results on the transport and dissipation of enstrophy in 2D incompressible flows. Enstrophy is half the space integral of vorticity squared, and it is a relevant quantity in 2D turbulence.  I  consider initial  data with vorticity in L² and its logarithmic refinements and study exact transport of enstrophy by the velocity field. I 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 Fihlo and Helena Nussenzveig Lopes.

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