There has been high scientific interest to understand the behavior of
the surface quasi-geostrophic (SQG) equation because it is a possible
model to explain the formation of fronts of hot and cold air and
because it also exhibits analogies with the 3D incompressible Euler
equations. It is not known at this moment if this equation can produce
singularities or if solutions exist globally. In this talk I will
discuss some recent works on the existence of global solutions.