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

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