Scattering and Blow-Up for the Focusing Nonlinear Klein-Gordon Equation with Complex Valued Data Below the Standing Waves
Speaker: Takahisa Inui, Kyoto University
Location: Warren Weaver Hall 1302
Date: Tuesday, March 10, 2015, 11 a.m.
We consider the focusing cubic nonlinear Klein-Gordon equation in 3-d space. It is well known that this initial value problem is locally well posed. So we are concerned with what initial values cause scattering or blow-up. Ibrahim, Masmoudi and Nakanishi gave a sufficient and necessary condition for the real valued solution with energy below the ground state to scatter or blow up. We will extend their result to complex valued solutions below the standing waves by using the charge. If time permits, we will consider an extension of the classification by the momentum.