Well-posedness and a numerical study of a regularization model with adaptive nonlinear filtering for incompressible fluid flow

We give a detailed analytical study of a Leray model of incompressible flow that uses nonlinear filtering based on indicator functions. The indicator functions allow for local regularization, instead of global regularization which can over-smooth and dampen out important flow structures. The key to the analysis is the identification of the indicator function as a Nemyskii operator. After proving well-posedness, we provide a numerical study which includes proving optimal convergence of finite element method for the model, as well as several numerical experiments.