Layer separation of the 3D incompressible Navier–Stokes equation in a bounded domain

We provide an unconditional L2 upper bound for the boundary layer separation of Leray–Hopf solutions in a smooth bounded domain. By layer separation, we mean the discrepancy between a (turbulent) low-viscosity Leray–Hopf solution uν and a fixed (laminar) regular Euler solution u¯ with similar initial conditions and body force. We show an asymptotic upper bound C||u¯||L∞3T on the layer separation, anomalous dissipation, and the work done by friction. 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.