Well-chosen Weak Solutions of the Instationary Navier-Stokes System and Their Uniqueness

We clarify the notion of well-chosen weak solutions of the instationary Navier-Stokes system recently introduced by the authors and P.-Y. Hsu in the article Initial values for the Navier-Stokes equations in spaces with weights in time, Funkcialaj Ekvacioj (2015). Well-chosen weak solutions have initial values in L2 ( ) contained also in a quasi-optimal space of Besov type of initial values such that nevertheless Serrin’s Uniqueness Theorem cannot be applied. However, we find universal conditions such that a weak solution given by a concrete approximation method coincides with the strong solution in a weighted function class of Serrin type