Vorticity interior trace estimates and higher derivative estimates via blow-up method

We derive several nonlinear a priori trace estimates for the 3D incompressible Navier-Stokes equation, which extend the current picture of higher derivative estimates in the mixed norm. The main ingredient is the blow-up method and a novel averaging operator, which could apply to PDEs with scaling invariance and $\varepsilon$-regularity, possibly with a drift.