Student Harmonic Analysis and PDE Seminar (HADES): Concentration Compactness Methods for Nonlinear Dispersive PDEs

Seminar | February 26 | 3:40-5 p.m. | 740 Evans Hall | Note change in date

 James Rowan, UC Berkeley

 Department of Mathematics

Concentration compactness methods provide a powerful tool for proving global well-posedness and scattering for nonlinear dispersive equations. Once one has a small-data global well-posedness result, one knows that there is some minimal size of the initial data at which global well-posedness and scattering can fail. Then, using a profile decomposition, one can show that there is a minimal blowup solution that is almost periodic. One can then use tools like long-time Strichartz estimates and interaction Morawetz inequalities to rule out these "minimal enemies." I will illustrate this technique by presenting a proof, due to Killip and Visan, of the global well-posedness and scattering for the three-dimensional energy-critical defocusing NLS.