PDE Seminar (2016/5/20): Global dynamics above the ground state energy for the combined power-type nonlinear Schr\”{o}dinger equations with energy-critical growth at low frequencies, Hiroaki Kikuchi (Tsuda College)

2016-5-20 16:30 - 2016-5-20 18:00
Faculty of Science Building #3, Room 309
Hiroaki Kikuchi (Tsuda College)
In this talk, we consider the nonlinear Schr\"{o}dinger equations with combined power-type nonlinearity which includes the energy-critical growth. Our aim is to classify the asymptotic behavior of the solutions. First, we review several results concerning the classification of the solutions whose energy is less than that of the ground state. Next, we consider the solutions which have a slightly greater than that of the ground state. In this case, we obtain a so-called nine-set theory developed by Nakanishi and Schlag (2012). This talk is based on a joint work with T. Akahori(Shizuoka), S. Ibrahim(Victoria) and H. Nawa (Meiji).