Finite-element-based Faedo–Galerkin weak solutions to the Navier–Stokes equations in the three-dimensional torus are suitable

AbstractIt is shown in this paper that Faedo–Galerkin weak solutions to the Navier–Stokes equations in the three-dimensional torus are suitable provided they are constructed using finite-dimensional spaces having a discrete commutator property and satisfying a proper inf–sup condition. Low order mixed finite element spaces appear to be acceptable for this purpose. This question was open since the notion of suitable solution was introduced