The 24th KMGS will be held on September 21st, Thursday, at Natural Science Building (E6-1) Room 1501.
We invite a speaker Uihyeon Jeong from the Dept. of Mathematical Sciences, KAIST.
The abstract of the talk is as follows.
Slot (AM 11:50~PM 12:30)
[Speaker] 정의현 (Uihyeon Jeong) from Dept. of Mathematical Sciences, KAIST, supervised by Prof. 권순식 교수님 (Soonsik Kwon)
[Title] Quantized slow blow up dynamics for the energy-critical co-rotational wave maps problem
[Discipline] Analysis
[Abstract]
In this talk, we consider the blow-up dynamics of co-rotational solutions for energy-critical wave maps with the 2-sphere target. We briefly introduce the (2+1)-dimensional wave maps problem and its co-rotational symmetry, which reduces the full wave map to the (1+1)-dimensional semilinear wave equation. Under such symmetry, we see that this problem has a unique explicit stationary solution, so-called “harmonic map”. Then we point out some of the works of analyzing the long-term dynamics of the flow near the harmonic map. Among them, we focus on the smooth blow-up result that corresponds to the stable regime. In particular, the case where the homotopy index is one has a distinctive nature from the other cases, which allows us to exhibit the smooth blow-up with the quantized blow-up rates corresponding to the excited regime.
[Language] Korean