On Local Uniqueness of Weak Solutions to the Navier–Stokes System with BMO −1 Initial Datum

We address the problem of local uniqueness of weak solutions to the Navier–Stokes system, with the initial datum in a subspace of $${BMO^{-1}(\mathbb{R}^{n})}$$ . The existence and uniqueness of local mild solutions has been proven by Koch and Tataru (Adv Math 157:22–35, 2001). We present a necessary and sufficient condition for two weak solutions to evolve from the same initial datum, and for weak solutions to be mild.