A constructed example of a linear Stokes flow inside a bounded domain (a sphere) with a Navier-slip boundary condition that exhibits anomalous dissipation: its mean viscous energy-dissipation rate stays bounded below by a positive constant as viscosity vanishes. The flow is driven by a fixed external forcing that is smooth in the interior but concentrates energy at the boundary on sets of Lebesgue measure zero. Because the construction is linear (no nonlinear vortex stretching) yet still dissipative in the inviscid limit, it demonstrates that the standard global anomalous-dissipation criterion does not by itself measure the contribution of the nonlinear convection term, contrasting with Kato-type no-anomalous-dissipation results under no-slip conditions.
Dudley and Trivisa construct an explicit example showing that anomalous dissipation can occur in a bounded interior domain. Anomalous dissipation is the persistence of a positive mean energy-dissipat…