Jincheng Yang, Department of Mathematics, The University of Chicago, USA

We provide an unconditional $L^2$ upper bound for the boundary layer separation of 3D Leray--Hopf solutions in a smooth bounded domain. By layer separation, we mean the discrepancy between a (turbulent) low-viscosity Leray--Hopf solution $u^\nu$ and a fixed (laminar) regular Euler solution $\bar u$ with initial conditions close in $L^2$. Layer separation appears in physical and numerical experiments near the boundary, and we bound it asymptotically by $C \|\bar u\|_{L^\infty}^3 t$. This extends the previous result when the Euler solution is a regular shear in a finite channel. The key estimate is to control the boundary vorticity in a way that does not degenerate in the vanishing viscosity limit.