The inviscid limit for non-smooth vorticity

We consider the inviscid limit of the incompressible Navier-Stokes equations for the case of two-dimensional non-smooth initial vorticities in Besov spaces. We obtain uniform rates of L^p convergence of vorticities of solutions of the Navier Stokes equations to appropriately mollified solutions of Euler equations. We apply these results to prove strong convergence in L^p of vorticities of Navier-Stokes solutions to vorticities of the corresponding, not mollified, Euler solutions. The short time results we obtain are for a class of solutions that includes vortex patches with rough boundaries and the long time results for a class of solutions that includes vortex patches with smooth boundaries.