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 Lp 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 Lp 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.
All Science Journal Classification (ASJC) codes