Carlos E. Kenig, University of Chicago

Unique continuation for evolution equations.

We will discuss some recent unique continuation results for parabolic and dispersive equations. The results for parabolic equations are due to Escauriaza, Seregin and Sverak, and have been applied by them to regularity of weak solutions to Navier-Stokes. The results for dispersive equations are due to Kenig-Ponce-Vega, and Ionescu-Kenig, and they have applications to control theory questions,and it is hoped that they will be useful for the study of regularity of solutions to critical non-linear Scrhodinger equations, in analogy with the work of Escauriaza, Seregin and Sverak.