Seminar

We present a strategy to solve globally in time some nonlinear PDEs at higher order Sobolev regularity, by relying exclusively on energy estimates. The main point is the introduction of suitable modified energies that allow us to control the higher order Sobolev norms for large times. We shall focus mainly on NLS and nonlinear Half-Wave. Moreover, by using some extra basic informations coming from the dispersion (when available), one can get new results on the polynomial growth of higher order Sobolev norms. The talk is based on a joint work with T. Ozawa (Waseda U.) and on a work in progress with F. Planchon (Nice U.).