Suitable weak solutions of the Navier-Stokes equations constructed by a space-time numerical discretization

摘要

We prove that weak solutions obtained as limits of certain numericalspace-time discretizations are suitable in the sense of Scheffer andCaffarelli-Kohn-Nirenberg. More precisely, in the space-periodic setting, weconsider a full discretization in which the theta-method is used to discretizethe time variable, while in the space variables we consider appropriatefamilies of finite elements. The main result is the validity of the so-calledlocal energy inequality.