Event Type:

Applied Mathematics and Computation Seminar

Date/Time:

Friday, January 7, 2011 - 04:00 to 05:00

Location:

GLK 113

Event Link:

Abstract:

We will discuss the Cauchy Problem for a class of quasilinear

Schr\"odinger equations in which the second order terms do not need to be

elliptic. We will outline the local in time existence results for initial

data in appropriate Sobolev spaces. This work build on the work on previous

work as well as the papers of C. Kenig, G. Ponce, L. Vega, and C. Roulvung.

We show that under appropriate conditions it is not necessary to require the

initial data to lie in weighted Sobolev spaces in order to have local in

time existence.