  We deal with the incompressible Navier-Stokes equations, in two and three
dimensions, when some vortex patches are prescribed as initial data i.e. when
there is an internal boundary across which the vorticity is discontinuous. We
show -thanks to an asymptotic expansion- that there is a sharp but smooth
variation of the fluid vorticity into a internal layer moving with the flow of
the Euler equations; as long as this later exists and as t * nu is small, where
nu is the viscosity coefficient.
