Recent progress on semi-linear wave equations on $\mathbb{R}^{3+1}$
Time: 2017-10-16
Published By: Ningbo Lu
Speaker(s): Jianwei Yang （BICMR）
Time: 10:00-11:30 October 18, 2017
Venue: Room 29, Quan Zhai, BICMR
Recent progress on semi-linear wave equations on $\mathbb{R}^{3+1}$
(after the authors Grillakis, Kenig, Merle, Duyckaerts ....)
Abstract:
In the past 30 years or so, there has been considerable interest in the study of nonlinear wave equations, especially on the long-time dynamics for the solutions with large initial data, such as the scattering theory, blow-up phenomena, etc., culminating the celebrated settlement of the "soliton resolution conjecture" for energy critical nonlinear wave equation in spherical symmetric variables. In this talk, we will briefly recall these results and several recent progress, focusing on the energy sub-critical and supercritical nonlinear growth. In particular, I will present a work that I did in collaboration with Thomas Duyckaerts with some of the details of the proof included.
(after the authors Grillakis, Kenig, Merle, Duyckaerts ....)
Abstract:
In the past 30 years or so, there has been considerable interest in the study of nonlinear wave equations, especially on the long-time dynamics for the solutions with large initial data, such as the scattering theory, blow-up phenomena, etc., culminating the celebrated settlement of the "soliton resolution conjecture" for energy critical nonlinear wave equation in spherical symmetric variables. In this talk, we will briefly recall these results and several recent progress, focusing on the energy sub-critical and supercritical nonlinear growth. In particular, I will present a work that I did in collaboration with Thomas Duyckaerts with some of the details of the proof included.
