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

TL;DR

This paper develops new nonlinear a priori trace estimates for the 3D Navier-Stokes equations using a blow-up method and averaging operator, advancing understanding of higher derivative bounds in fluid dynamics.

Contribution

It introduces a novel blow-up approach and averaging operator to derive nonlinear trace estimates, extending higher derivative regularity results for Navier-Stokes equations.

Findings

Derived nonlinear a priori trace estimates for 3D Navier-Stokes

Extended the framework of higher derivative estimates in mixed norms

Applicable to PDEs with scaling invariance and $\\varepsilon$-regularity

Abstract

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.