On the construction of suitable solutions to the Navier-Stokes equations and questions regarding the definition of large eddy simulation

This paper discusses the notion of large eddy simulation (LES) as a mathematical concept and proposes to use the concept of suitable weak solutions as a building block for the development of a mathematical theory of LES. Various techniques for constructing suitable weak solutions to the three-dimensional Navier-Stokes equations are reviewed and many features of these mathematical constructions are shown to comply with well-accepted heuristic characterizations of LES.