Vanishing boundary geometry and critical pressure compactness for the three-dimensional Navier--Stokes equations

We develop a boundary blow-up scheme for the three-dimensional nonstationary Navier--Stokes equations in domains whose local boundary graphs belong to $W^{2-1/P_b,P_b}(\mathbb R^2)$ with $P_b>3$. The argument is designed to remove the $P_b>15/4$ restriction in the boundary partial-regularity theorem