The APDE seminar on Monday, 1/26, will be given by our own Sung-Jin Oh (UC Berkeley) in-person in Evans 736, and will also be broadcasted online via Zoom from 4:10pm to 5:00pm PST. To participate, please email Adam Black (adamblack@berkeley.edu).

Title: A physical-space approach to global asymptotics for variable-coefficient Schrödinger equations

Abstract: In this talk, I will discuss a new physical-space approach to establish the time decay and global asymptotics of solutions to variable-coefficient Schrödinger equations in (3+1)-dimensions. A key innovation in our methodology is the concept of a “good commutator,” which extends the classical commuting vector field method, and which combines well with Ifrim-Tataru’s testing by wave packets. As an immediate nonlinear application, we obtain new small data global existence and asymptotics results for quasilinear Schrödinger equations with cubic, Hamiltonian nonlinearity, variable coefficients in their linear part, and possibly outside obstacles. This talk is based on an upcoming work with F. Pasqualotto (UCSD) and N. Tang (UC Berkeley).