Summary: 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 the Navier-Stokes solutions to vorticities of the corresponding, not mollified, Euler solutions. The obtained short time results can be applied to a class of solutions that includes vortex patches with rough boundaries, and the long time results to a class of solutions that includes vortex patches with smooth boundaries.