Speaker：Prof. Hao Jia（University of Minnesota）

Time：2018.05.22, 10:00-12:00

Place：N212

Abstract:

In this talk we will discuss some recent progresses on the study of dynamics of energy critical wave equations, specifically on the soliton resolution conjecture (SRC). SRC predicts that for many dispersive equations, generic solutions should asymptotically de-couple into solitary waves and radiation as time goes to infinity. The conjecture is open for most equations except integrable ones, but is better understood in the case of energy critical wave equations. We will give a sketch of the proof of this conjecture for a sequence of times, in the case of semilinear wave equations. The proof uses many ideas, including optimal perturbation theory, monotonicity formula, unique continuation property for elliptic equations, and most interestingly a channel of energy argument for outgoing waves.