The HADES seminar on Tuesday, October 13th will be given by Dongxiao Yu via Zoom from 3:40 to 5 pm.

Speaker: Dongxiao Yu

Abstract: In this talk, I will discuss the long time dynamics of a scalar quasilinear wave equation in three space dimensions. This equation satisfies the weak null condition introduced by Lindblad and Rodnianski, and it admits small data global existence which was proved by Lindblad. I will present a proof of the existence of the modified wave operators for this quasilinear wave equation. This is accomplished in three steps. First, we derive a new reduced asymptotic system by modifying Hörmander’s method. Next, we construct an approximate solution to the quasilinear wave equation by solving the reduced system given some scattering data. Finally, we prove that the quasilinear wave equation has a global solution which agrees with the approximate solution at infinite time.