We address the problem of local uniqueness of weak solutions to the Navier-Stokes system, with the initial datum in a subspace of BMO -1ℝn). 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.
All Science Journal Classification (ASJC) codes
- Mild solutions
- Navier-Stokes equations
- Weak solutions