A dynamical approach to large eddy simulation of turbulent flows: existence of weak solutions

We consider a system of equations coming from turbulence models using a large eddy simulation (LES) technique. The idea of this approach bases on decomposing the velocity into a part containing large flow structures and a part consisting of small scales. The equations for large-scale quantities are derived from the Navier-Stokes equations with an additional constitutive relation for the contribution of small eddies. The mathematical difficulties in this paper focus on the non-linear and non-local turbulent term.