LOWER AND UPPER BOUNDS TO THE CHANGE OF VORTICITY BY TRANSITION FROM SLIP- TO NO-SLIP FLUID FLOW

摘要

For the transition from slip-to no-slip fluid flow, we establish lower and upper bounds to the resulting change of the L~2-norm of the vorticity. Moreover we present a transport-diffusion splitting scheme, built up solely by a transport step and subsequent diffusion step (without any additional vorticity creation operator as introduced in former studies by Lighthill, Marsden, and Chorin), the splitting scheme being consistent with the Navier-Stokes equations with no-slip condition.