The Analysis and PDE Seminar will take place on Monday, September 26, in room 740, Evans Hall, from 4:10-5:00 pm.

Speaker: Satoshi Masaki

Title: Minimization problems on non-scattering solutions to NLS equation

Abstract: We consider global dynamics of focusing nonlinear Schrodinger equations. A first step in this direction is small data scattering which tells us that solutions around the zero solution asymptotically behave like free solutions. On the other hand, there exists non-scattering solutions such as standing waves and blowing-up solutions.

In this talk, we will seek threshold solutions between scattering solutions around zero and solutions with other behaviors, by introducing two minimization problems on non-scattering solutions. In particular, our main interest is the analysis of mass-subcritical case, in which the ground states are stable. The analysis of the minimization problems are based on concentration compactness/rigidity argument initiated by Kenig and Merle.