= Boundary layer
{wiki}
A <boundary layer> is a thin region next to a surface in which <viscosity> remains significant even when <inertia> dominates the outer <fluid flow>. Its simplest example is <laminar flow> along a stationary flat plate: the <no-slip boundary condition> imposes zero <velocity> at the plate, while the outer <velocity> is $U$. The resulting thin <velocity profile> contains a large normal <velocity> <gradient>, so small <dynamic viscosity> can still produce appreciable <wall shear stress>. The <Blasius boundary layer> makes this competition quantitative and explains how a plate aligned with the incoming <fluid flow> acquires <drag>.
The same balance appears in a <singular perturbation> of a <differential equation>: large <derivatives> in a thin region can keep a term with a small coefficient significant. For $\epsilon y''+y'=0$ on $[0,1]$ with $y(0)=0$ and $y(1)=1$, the <inner variable> $X=x/\epsilon$ resolves a left <boundary layer> of width $O(\epsilon)$.
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