Anomalous dissipation, i.e. the non-vanishing of the dissipation term in the limit of zero viscosity, is a cornerstone of turbulence theory. In the case of periodic, two-dimensional, incompressible fluid flow there has been a lot of recent work in which anomalous dissipation is ruled out if the vorticity, which is the curl of velocity, is p-th power integrable or even a nonnegative Radon measure. The vanishing viscosity limit in domains with boundary is a classical open problem due mostly to the formation of large gradients near the walls. These may propagate into the bulk of the fluid through boundary layer separation and have the potential to yield anomalous dissipation. In this talk we will discuss the absence of local anomalous dissipation in the vanishing viscosity limit in a bounded domain.
Co-authors: Tobias Barker, Milton Lopes Filho
De Matthew Juniper
De Sergey Gavrilyuk
De David Lannes
