Anomalous Dissipation for the Forced 3D Navier–Stokes Equations

In this paper, we consider the forced incompressible Navier–Stokes equations with vanishing viscosity on the three-dimensional torus. We show that there are (classical) solutions for which the dissipation rate of the kinetic energy is bounded away from zero, uniformly in the viscosity parameter, while the body forces are uniformly bounded in some reasonable regularity class.