  Using extrapolation theory, we develop a new framework to prove the
uniqueness of solutions for transport equations. We apply our methodology to
unify and extend the classical results of Yudovich and Vishik for 2D Euler
equations. In particular, we establish the uniqueness for the Euler flow whose
vorticity belongs to new scales of function spaces that contain both Yudovich
spaces and BMO. We give a self contained presentation.
