微分方程式セミナー


2018/6/29(Fri)

16:30--18:00 数学教室 大セミナー室(E301)

Jason Murphy

Missouri University of Science and Technology

Scattering below the ground state for nonlinear Schr\"odinger equations

The ground state solution to the nonlinear Schr\"odinger equation (NLS) is a global, non-scattering solution that often provides a threshold between scattering and blowup. In this talk, we will discuss scattering below the ground state for the focusing 3d NLS. This result was originally proved by Holmer--Roudenko and Duyckaerts--Holmer--Roudenko via the concentration-compactness approach to induction on energy. We will discuss new, simplified proofs of scattering below the ground state threshold that avoid the use of concentration-compactness altogether. This is joint work with B. Dodson.