ABSTRACT
In this chapter, we describe some further ways to approximate the Navier–Stokes equations that have been developed in the mathematical literature since the seminal work of Leray [276]. Some of them have been developed not as approximations but as corrections of the Navier–Stokes equations; in that case, one should be careful to respect the basic rules of Newtonian mechanics such as Galilean invariance or the material indifference principle. Others have been developed as simple discretization schemes for the numerical resolution of the equations: we present them in the setting of the whole space while they were developed in the setting of a bounded domain; we will miss some compactness properties useful to prove convergence, and we shall not address the delicate problem of defining the boundary conditions for the approximated problem.
