  Presented is a backward uniqueness result of bounded mild solutions of 3D
Navier-Stokes Equations in the whole space with non-trivial final data. A
direct consequence is that a solution must be axi-symmetric in $[0, T]$ if it
is so at time $T$. The proof is based on a new weighted estimate which enables
to treat terms involving Calderon-Zygmund operators. The new weighted estimate
is expected to have certain applications in control theory when classical
Carleman-type inequality is not applicable.
