Spectral Methods in PDE

Abstract

This is to review some recent progress in PDE. The emphasis is on (energy) supercritical nonlinear Schrödinger equations. The methods are applicable to other nonlinear equations.

arXiv commentThis is an invited contribution to Milan J. Math., after a talk at the Seminario Matematico e Fisico di Milano. It also contains a new result on critical Sobolev exponent for the cubic nonlinear Schrödinger equation on general surfaces. (13pp)