On the vanishing viscosity limit for 2D incompressible flows with unbounded vorticity

We show strong convergence of the vorticities in the vanishing viscosity limit for the incompressible Navier-Stokes equations on the two-dimensional torus, assuming only that the initial vorticity of the limiting Euler equations is in L ( p ) for some p > 1. This substantially extends a recent result of Constantin, Drivas and Elgindi, who proved strong convergence in the case p = infinity. Our proof, which relies on the classical renormalisation theory of DiPerna-Lions, is surprisingly simple.