Holderian regularity of the viscous vortex patches

We study the evolution of the Holderian regularity for some convection-diffusion equation with respect to Lipschitzian vector field, generalizing an earlier result for the Besov spaces B-p(,infinity)s, with p finite and s is an element of (- 1, 1). As an application, we show for the two-dimensional Navier-Stokes system that if the initial vorticity is a vortex patch having a C1+is an element of boundary then its image through the viscous flow preserves this regularity for all time with uniform control on the viscosity. We also show some results of inviscid limit. (C) 2004 Academie des sciences. Publie par Elsevier SAS. Tons droits reserves.