We prove existence of weak solutions to the model. In other words, it begins to consider well-posedness of the model without using this extra regularization. This report took a long time to complete, but it's done at last. Soon it will be available for download hhere. W. Layton, Bounds on energy dissipation rates of the large eddies in turbulent shear flows, technical report,June, 2000.
Shear flows are very important in experimental turbulence studies.
Thus, they have also attacted analytical attention, in spite of the fact that they are less mathematically 'convenient' than models with homogeneous Dirichlet boundary conditions. In 3d there has recently been considerable work bounding the average energy dissipation rate in the NSE for shear flows. Thus, it's interesting to understand the average energy dissipation rates in various large eddy models. This can be used for example to assess and compare models mathematically. This report begins the study of energy dissipation rates in 'large eddy fluids'.