Remark on uniqueness of weak solutions to the navier-stokes equations

Consider the Navier-Stokes equations with the initial value a and the external force with 2/s + njq < 3. Let v and u be two weak solutions with the same data a and f. If v satisfies the usual energy inequality and if, then we have v = u.Beiräo da Veiga, H., An extension of the classical Prodi-Serrin's condition for the Navier-Stokes equations in Rⁿ. Preprint, Pisa, 1995.