From Brezis-Gallouet to the polynomial growth of Sobolev norms

Professor: Nicola Visciglia, University of Pisa, Italia

Abstract
As a first step we recall the classical approach by Brezis and Gallouet to cubic NLS in 2D. Nest we show a recent result obtainedin collaboration with T. Ozawa where we prove global well-posedness for the fourth order NLS in 2D, by using exclusively energy estimates.This technique is rather useful especially in other contexts where there is not dispersion:typically the half-wave equation. We also present a refinement of this technique in order to get new results on the polynominal growth of higher order Sobolev norms for soluctions to 2D NLS on general compact manifolds. This last result is in collaboration with F. Planchon.

Youtube Playlist:

DOWNLOAD

Class 01 - 21-07-2015 - download
Class 02 - 22-07-2015 - download
Class 03 - 23-07-2015 - download

________________________________________________________________________________