The Existence of Anomalous Dissipation over Bounded Interior Domains

A prevalent feature of three-dimensional turbulence is the presence of anomalous dissipation, or that the mean rate of energy dissipation is bounded below by a positive number in the inviscid limit. This is thought to be due to the nonlinear convection term in the Navier Stokes equations stretching vortex tubules and thereby increasing the amount of small scale oscillations within the flow. In this paper, we construct an example of a linear Stokes flow within a sphere that exhibits anomalous dissipation.