Régularité höldérienne des poches de tourbillon visqueuses

We study the evolution of the Hölderian regularity for some convection-diffusion equation with respect to Lipschitzian vector field, generalizing a result of R. Danchin [J. Math. Pures Appl. 76 (1997) 609] for the Besov spaces Bp,∞s, with p finite and s∈(−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+ɛ boundary then its image through the viscous flow preserves this regularity for all time. We also show some results of inviscid limit.