The celebrated work of Leray (eighty years ago) settled the basic questions concerning the well-posedness of the Navier-Stokes equations in the plane (two dimensions). However, the basic premise of this work was the assumption that the initial velocity field is (at least) locally square integrable (namely, locally finite kinetic energy).
Thus, some primary fluid dynamical objects (notably point vortices) have been excluded (as they generate non square integrable velocities).
The topic of well posedness of such flows has been taken up only some twenty five years ago, and the final uniqueness result was obtained by Gallagher and Gallay five years ago.
In this talk we review the story of such flows, including basic open problems concerning the behavior of steady state solutions in bounded domains.