# Mathematics Colloquia and Seminars

We will introduce the boundary layer theory, a classical topic in fluid dynamics, and survey a few recent results. We will culminate with the following result, obtained in collaboration with Yan Guo: Consider the vanishing viscosity limit for the 2D steady Navier-Stokes equations in the region $0\le x\le L$ and $0 \le y \le \infty$ with no slip boundary conditions at $y=0$. For $L\ll 1$, we justify the validity of the steady Prandtl layer expansion for scaled Prandtl layers, including the celebrated Blasius boundary layer.