The growth mechanism of boundary layers for the 2D Navier-Stokes equations

Abstract

We give a detailed description of formation of the boundary layers in the inviscid limit problem. To be more specific, we prove that the magnitude of the vorticity near the boundary is growing to the size of $1/\sqrt{\nu }$ and the width of the layer is spreading out to be proportional the $\sqrt{\nu }$ in a finite time period. In fact, the growth time scaling is almost ν.