UNIQUENESS OF WEAK SOLUTIONS OF THE NAVIER-STOKES EQUATIONS IN L-N(OMEGA)

We prove the uniqueness of weak solutions of the Navier-Stokes equatio ns in C([0, T); L-N (Omega)), where Omega is The whole space R-N a reg ular domain of R-N or the torus T-N, with N greater than or equal to 3 . The proof lies on three elementary ingredients: the introduction of a dual problem, a decomposition of the solutions and a ''boostrap'' ar gument. (C) Academie des Sciences/Elsevier, Paris.