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

Abstract

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 Lp for some p > 1. This substantially extends a recent result of Constantin, Drivas and Elgindi, who proved strong convergence in the case p = ∞. Our proof, which relies on the classical renormalisation theory of DiPerna–Lions, is surprisingly simple.