Dongho Chae 

On the one-dimensional model of the quasi-geostrophic equation

In this talk we present results on the analysis of a 1D model of the
quasi-geostrophic equation. We show the existence of singularities
in finite time for the equation.  For the critical viscosity case
singularities form when the $L^{\infty}$ norm of the initial data
is bigger than the viscosity, conversely there is absence of
singularities. In the second order viscosity case  we obtain
globally smooth, exact solutions for any value of the viscosity.
This is a joint work with A. Cordoba, D. Cordoba and M. Fontelos.