**Susan Friedlander**

**Afilliation:**Mathematics Department, University of Southern California

**Title:**Well/Ill-Posedness Results for the Magneto-Geostrophic Equations

**Abstract:**We consider an active scalar equation with singular drift velocity that is motivated by a model for the geodynamo. We show that the non-diffusive equation is ill-posed in the sense of Hadamard in Sobolev spaces. In contrast, the critically diffusive equation is globally well-posed.

The spatial anisotropy of the equation gives rise to some interesting novel effects which we discuss in the context of the equation with fractional diffusion.

This work is joint with Vlad Vicol.