分野別セミナー

We study growth of higher Sobolev norms of solutions to the
one-dimensional periodic nonlinear Schrodinger equation (NLS). It
is well-known that growth of Sobolev norm is at most polynomial
rate by Bourgain, and other works. Here we use the normal form
reduction and the upside-down I-method to reprove this and
improve known result for some case. I will discuss the idea of
normal form reduction and how we combine that with upside-down
I-method. This is a collaboration with Jim Colliander and
Tadahiro Oh.