Past lectures

Abstract

In this class we will study local and global existence of solutions to geometric dispersive equations. We will consider wave maps and Schrödinger maps as our basic models. We will develop various estimates for the associated linear problems, and we will show how these estimates can be applied to the nonlinear equations.

Topics to be covered include

- basic theory of linear wave and Schrödinger equations

- existence of solutions for wave maps in arbitrary dimension

- existence of solutions for Schrödinger maps

- frame formulation of these equations of weak solutions

- blowup and formation of singularities